IT MAY BE a kind of lunacy, a moonlight madness. Or perhaps it's just spring fever. But at midnight Saturday, two hours after the full moon rises over the Capitol, the Potomac Appalachian Trail Club will begin its annual late-night Moon Walk tour of the Mall.

The walk, free and open to all, is for anyone who wants to see Washington's familiar monuments in a different light and celebrate spring's shortest night -- when Daylight Saving Time begins and clocks are turned ahead one hour.

It includes a tour of Union Station; a visit to the Botanic Garden; and a bluegrass-country music concert on the lawn near Arlington Cemetery. The six-mile walk then crosses Key Bridge at dawn, and everyone disbands or repairs to all-night Georgetown restaurants for breakfast.

Earlier Saturday night, starting at 10 p.m., the Washington Area Bicyclist Association will hold its third annual Moon Ride, a free, two-hour, 10-mile expedition through upper Rock Creek Park on quiet stream-valley roads.

Those are just two of the night-time opportunities for rambling outdoors around Washington. There are also boat trips on the Potomac, park hikes, observatory tours, guided tours of the Washington, Lincoln and Jefferson memorials and the Old Post Office and camping at a dozen scenic public campgrounds nearby. MIDNIGHT TO DAWN

The Moon Walk begins at Union Station at midnight, when the last Metro subway trains pass through. Special features are a 12:15 a.m. tour of the station, now being renovated; a 2 a.m. floral visit to the Botanic Garden (now bright with orchids, lilies and hydrangeas); and a 4 a.m. concert on the lawn near Arlington Cemetery by the Dawson Singers, a seven-member, gospel/bluegrass/country music group, which includes guitars, banjo and dulcimer.

"We've played at retirement homes, St. Elizabeths . . . lots of places, but we've never done a 4 a.m. sunrise serenade," says founder and guitarist Bob Dawson.

The Moon Walk also passes the Capitol and the Mall's memorials, offering the chance to see the magnificent reflections in the pools at the foot of the Capitol and the Lincoln Memorial.

In addition, the post-midnight views of the Lincoln and Jefferson memorials, when only soft interior lights silhouette the statues, are among the most memorable and most photographed.

But perhaps the most unusual feature of the midnight-to-dawn walk is discovering a silent Washington. The constant background noise of city traffic and airplanes is gone and the peaceful Mall has the feel of the 19th century -- when cattle roamed meadows in front of the Smithsonian Castle and the White House, Constitution Avenue was a canal and the president would occasionally slip down to the Potomac for a late night swim.

The loudest sounds may be the crunching of feet on gravel Mall paths.

(The man behind the Moon Walk is Hal Brayman, who during the day is assistant staff director on the Senate Committee on the Environment and Public Works: "I just volunteered six months ago when someone said, 'Hey, let's have a night hike.' I got Union Station people to agree to a tour. Then the architect of the Capitol, George White, agreed to open the Botanic Garden . . . He's a great walker and has hiked the Himalayas . . . And then I remembered that Bob Dawson, an assistant sectretary of the Army, has this music group. And that was it."

(The sponsoring Potomac Appalachian Trail Club, which also owns rustic log cabins in the Blue Ridge Mountains and leads weekly mountain hikes, can be reached weekdays at 638-5307 and weeknights from 7-10 p.m. at 638-5306.) ROLLING ALONG ROCK CREEK

The Moon Ride through upper Rock Creek Park offers two hours and 10 miles of bicycling along some of the most scenic and a few of the hilliest sections of the federal government's oldest urban park.

The leisurely ride starts at 10 p.m., just as the moon is rising. Cyclists are required to have bike lights and are urged to wear helmets.

The jump-off point is the parking lot of the Carter Barron Amphitheater and National Park Service Tennis Stadium at 16th and Kennedy streets NW. Riders descend Morrow Drive into Rock Creek Park, climb Glover Road (formerly Ridge Road) and Ross Drive and then follow Beach Drive along Rock Creek up into Montgomery County -- then back down Beach Drive to Morrow Drive.

The Rock Creek stream valley has Washington's largest variety of wildlife -- including foxes and occasional deer; beaver and muskrat along the creek; and many nocturnally active birds, among them the loquacious mockingbird and nighthawk (a relative of the whippoorwill) and at least four varieties of owl, from great horned to screech and saw-whet. (Night cyclists no longer need fear the wolves, bison, black bear and Algonkian Indians that once roamed Rock Creek.)

The ride coincides with the National Park Service's auto ban, which begins this weekend on about five miles of Beach Drive and West Beach Drive and will be in effect year-round from now on. The auto ban, originally just for the warmer months, was instituted four years ago to enable cyclists, joggers and hikers to enjoy the scenic sections of the park where there is no bicycle trail. It extends from 7 a.m. Saturdays to 7 p.m. Sunday nights.

Washington's last organized moonlight bicycle ride, held two years ago on the Mall by American Youth Hostels, attracted more than 3,000 cyclists and turned out to be the largest single cycling event in recent Washington history -- though nothing like the mammoth (daytime) bicycle parades held on Pennsylvania Avenue at the turn of the century.

(The Moon Ride's sponsor, the Washington Area Bicyclist Association, is a nonprofit group that lobbies for cyclists and sponsors bike events like Washington's annual Bike to Work Day -- May 1 this year. It can be reached weekdays, 9 a.m. to 6 p.m., at 544-5349. It also has a taped telephone message on bike events at that number.) ALSO ON THE NIGHT SIDE

Other night activities around the area include: STARGAZING

U.S. NAVAL OBSERVATORY, Massachusetts Avenue and 34th Street NW. Heavenly views of the moon, planets and stars every Monday night except federal holidays. Tour also includes a visit to the nation's master clock, which keeps time for the United States. The best views of the moon are not when it's full because it is so bright. Free passes are given to the first 140 people at the observatory gate at 8:30 p.m. (DST). 653-1543.

UNIVERSITY OF MARYLAND OBSERVATORY, Metzerott Road in College Park, opposite the university administration building. The observatory has a free open house the 5th and 20th of each month from 9 to 11 p.m. There is a brief slide show and then skyviews through four telescopes. The observatory can hold several hundred people. 454-3001. BOAT TOURS

WASHINGTON BOAT LINE, at Pier 4 on the Maine Avenue waterfront, has high school dance cruises on the Potomac River Thursday and Sunday nights, adult dance cruises Tuesday and Friday nights and a city lights river cruise on Sunday nights. Boats range from a small canal boat to a large sternwheeler that holds 550 people. The cruises usually extend from Georgetown to Alexandria. The three-hour student dance cruises, with a disc jockey and a snack bar, start at 7:30 p.m. and cost $10.75 per person. The three-hour adult dance cruises start at 8:30 p.m. include a cash and snack bar and cost $12.50 Tuesday nights and $14 Friday nights. The two-hour city lights cruise also has cash and snack bars and costs $8. 554-8011.

POTOMAC PARTY CRUISES, at the foot of Prince Street in Alexandria, features 3- to 3 1/2-hour dinner cruises nightly on the Dandy from Alexandria up to the Kennedy Center. The cruises leave at 7:30 p.m. and cost $40 per person on weeknights and $45 on weekends. 683-6076.

POTOMAC RIVER BOAT CO., at the foot of Queen Street in Alexandria, offers charters on the paddle wheeler Cherry Blossom, which also has monthly Sunday brunch cruises. 684-0580. MEMORIAL AND BUILDING TOURS

WASHINGTON MONUMENT, LINCOLN, JEFFERSON & VIETNAM MEMORIALS are lighted and have free nightly guided tours by National Park Service rangers until midnight. There is also a nightly 7 p.m. tour of the catacombs beneath the Lincoln Memorial for small groups. It is by reservation only and is booked through the summer. Call 426-6841 for information on all Park Service tours.

OLD POST OFFICE, at Pennsylvania Avenue and 12th Street NW. National Park Service rangers provide free tours to the tower and its observation deck daily from 8 a.m. to 11 p.m., except Thursday nights when the tower is closed for bell-ringing practice by the Washington Ringing Society. 523-5691. PARK TOURS

NORTHERN VIRGINIA REGIONAL PARK AUTHORITY conducts occasional night outdoor naturalist tours. Coming tours include a July 12, 9:30 p.m. stargazing trip with naturalists at Algonkian Regional Park on the Loudoun-Fairfax County border and an Aug. 16, 8 p.m. night creatures trail hike at Potomac Overlook Regional Park in north Arlington. 352-5900.

FAIRFAX COUNTY PARK AUTHORITY has occasional night park events, including a free "Leave It to Beaver" boardwalk and marsh hike this Saturday from 6 to 8 p.m. at Huntley Meadows Park on Lockheed Boulevard in Hybla Valley, off U.S. 1. 768-2525. CAMPGROUNDS

This area has a baker's dozen scenic and moderately priced public campgrounds within less than an hour's drive, most with campsites near lakes, streams or rivers. All have restrooms and most have hot showers. NATIONAL PARK SERVICE

C&O CANAL NATIONAL HISTORICAL PARK has hiker-biker overnight camping areas for tent camping along the towpath roughly every five miles along its 185-mile length, starting 10 miles outside Georgetown. Sites have toilets and most have water. However, the park and campsites are temporarily closed because of last fall's flood damage to the canal. 301/739-4200).

GREENBELT PARK, 12 miles from downtown Washington off the Baltimore-Washington Parkway, at Greenbelt Road exit. It has 174 family camping sites open year round, for tents, trailers or recreational vehicles. There are fireplaces, tables and restrooms for campsites, but no showers or electricity. Rates are $4 a night. No reservations. 344-3948 or 344-3943. PRINCE WILLIAM FOREST PARK, 32 miles south of Washington off I-95 (at Rte. 619), has 120 tent camping sites and 100 trailer and recreational vehicle sites available on a first-come, first-served basis. It has hot showers and even a coin-operated laundry. Tent camping is $4 a night, and $11 a night for trailers and recreational vehicles that want electric and water hook-ups. 703/221-7181. MARYLAND NATIONAL CAPITAL PARK AND PLANNING COMMISSION

CABIN JOHN REGIONAL PARK on Tuckerman Lane near Montgomery Mall in Montgomery County. Primitive tent sites, "just clear spots in the woods," are available to Montgomery and Prince George's County residents only at 50 cents a night. Reservations may be made by phone (565-7417), but campers must also register at the commission office, 9500 Brunett Ave., Silver Spring.

LITTLE BENNET REGIONAL PARK in upper Montgomery County, with 3,700 acres one of the largest parks in the region (Clarksburg exit from I-270, left at Clakrsburg on Rte. 355 to entrance). It has 91 campsites, 25 with electricity. Campsites are $5 a night ($7 with electricity) for Montgomery and Prince George's County residents and $2 more for nonresidents. 972-9222.

LOUISE F. COSCA REGIONAL PARK, near Clinton in Prince George's County on Woodyard Road off Rte. 5. There are 25 family woodland campsites open year-round and two large group campsites at discount rates. Heated restrooms and showers. Rates are $4 a night, plus $2 extra for electric outlets and $2 for water connections. No reservations. 301/868-1397.

PATUXENT RIVER PARK, also known as Mount Calvert Regional Park, near Upper Marlboro in Prince George's County, about 35 minutes from the Beltway (south on U.S. 301 from Upper Marlboro; left on Croom Station Road Rte. 382 to Croom Airport Road, which ends in the park). A half-dozen large camping areas and some isolated semi-primitive campsites for backpackers are available year round, all close to the Patuxent River. Campsites are $1 a night for Montgomery and Prince George's County residents and $1.25 for nonresidents. 627-6074. STATE OF MARYLAND

CEDARVILLE NATURAL RESOURCES MANAGEMENT AREA, in southern Prince George's County just east of intersection of Rtes. 301 and 5. Forest area with 130 campsites open year round. Restrooms and hot showers. No reservations. Rates are $6 a night for Maryland residents and $7 for nonresidents. No electric outlets for trailers. 301/888-1622.

PATAPSCO VALLEY STATE PARK, north of Baltimore-Washington International Airport, about 30 miles from Washington. About 100 campsites in wooded river valley within short walk of Patapsco River. No reservations. Showers and restrooms but no electric outlets for trailers. Rates are $6 for state residents, $7 for out-of-state residents. 301/461-5005. NORTHERN VIRGINIA REGIONAL PARK AUTHORITY

BULL RUN REGIONAL PARK, along Bull Run south of Manassas National Battlefield Park (Centreville exit of I-66; west on U.S. 29 for three miles). It has 150 campsites, 40 with electrical outlets. A swimming pool is open after Memorial Day. Campsites are $7.50 without electricity ($9 with) for three people, plus $1 for each additional camper. It will take reservations. A park entrance fee of $4 is charged nonresidents of Northern Virginia. 631-0550.

POHICK BAY REGIONAL PARK, on the Potomac River in Fairfax County 25 miles south of Washington off U.S. 1 on Gunston Hall Road (Rte. 242). There are 325 campsites, 103 with electrical outlets. Restrooms, showers, laundry facilities and a camp store. No reservations. A swimming pool opens Memorial Day. Campsites are $7.50 without electricity ($9 with) for three people, plus $1 for each additional camper. A park entrance fee of $4 is charged nonresidents of Northern Virginia. 703/339-6104). FAIRFAX COUNTY PARK AUTHORITY

BURKE LAKE PARK, on Ox Road (Rte. 123) south of Fairfax City. The park is open year round except Christmas Day. There are 163 campsites and five wilderness area campsites. No campsites have electricity. Sites are $7 a night, plus $1.50 for electricity. Wilderness sites are $8 for county residents, $16 for nonresidents. Reservations cost $3 extra. 323-6600 or 941-5008.

LAKE FAIRFAX PARK, near Reston, on Lake Fairfax Drive off Baron Cameron Avenue. There are 200 campsites open year round, about half with electric outlets. There are also a number of wilderness area campsites. Most park recreation facilities, including lake boating and a swimming pool, do not open till mid or late May. Campsites are $7 a night, plus $1.50 for electricity. Wilderness sites are $8 for county residents, $16 for nonresidents. Reservations are $3 extra. 471-5415 or 941-5008.