"THERE ARE TWO DEER up there," said a fellow golfer, pointing toward the far reaches of the driving range, cut off from view by a patch of woods. "They must know just how far we can hit the ball, 'cause they stay just out of range."

I never did get a look at those wily ones, but later that warm morning, as I approached the 18th tee, a doe appeared, about 300 yards down the fairway. She broke for the cover of woods, then suddenly reappeared with two fawns and trotted across the fairway to the far woods.

This occurred only two hours from Washington, in Cacapon State Park, where I have seen deer, as well as smaller wildlife, on just about every one of my dozen or so visits over the years. Cacapon, one of the 14 state parks in the West Virginia system, is the closest to Washington, just nine miles south of Berkeley Springs on Route 522, accessible from Maryland through Hancock or from Virginia through Winchester.

The main attraction for me always has been the golf. The 6,940-yard layout is one of the sport's best-kept secrets. Designed by famed golf architect Robert Trent Jones, it is a fine test of one's skills as well as being one of the most beautiful layouts in the East. Only the first two holes avoid the woods, and some of the high-ground spots give a spectacular view of the surrounding mountains. Yet, except on summer weekends, one hardly ever finds a crowd.

But golf is only one reason for visiting Cacapon. Its 6,115 acres include a man-made lake with a sandy beach and rental paddle boats, picnic areas, tennis courts, ballfields, playgrounds, fishing holes and hiking and bridle paths to the summit of Cacapon Mountain.

"We've got 10 horses at the stable," says Park Superintendent Phillip Dawson, who notes that all horseback riding must be supervised. "We don't want people getting lost."

There are 49 rental rooms in the main lodge, all with showers and television. The log-cabin inn, which was the original lodge when the site was first opened in the '30s, has 11 rooms in a more rustic setting with no television. The inn and lodge are open year-round.

For those who prefer more privacy, there are cabins -- 30 of them. Eleven are open all year, heated by a fireplace and forced-air furnace; 12, with fireplace only, are open from May through October; and seven, which have no heat, are open only from Memorial Day through Labor Day.

The cabins are in particular demand. Park officials take reservations 10 months ahead of time, and say it's wise to act that soon for planned summer weeks and fall weekends. From the second Monday in June until Labor Day, the cabins are rented by the week only; after Labor Day, rentals can be by the day, except for weekends, which must be for two nights. There is a lot of repeat business.

"A lot of people," says Dawson, "as soon as the 10-month period comes around, call up for their reservations."

However, you don't have to sleep at the park to enjoy its facilities. Many people come in for the day, or stay at area motels.

Much of the park is a product of the Depression. It was one of the original Civilian Conservation Corps camps in West Virginia in the late 1930s, Dawson says. "The lake and the standard cabins were built by the CCC."

Lest one get the impression that Cacapon is a quaint park on the outskirts of our urban sprawl, it should not be forgotten that the West Virginia panhandle can be wild country. Bears are not uncommon in the mountains. And there's plenty of other wildlife.

A few years ago, several of us had wandered to the side of a hill overlooking the 18th green to wait for friends finishing up a round of golf. Immediately as I sat down, I felt something on my lap -- a copperhead slithering away from the crowd that ha disturbed his rest. I didn't say anything until he left.

Encounters like that are unlikely these days, however. "We've cleared out the woods pretty good," says one of the park's maintenance officers. "Now the only snakes one is likely to encounter are water snakes near the golf course lake." CACAPON CAPERING

There is no admission charge to the park. Nature trails and picnicking are free but there are charges for various sports. Swimming is $2 adults, $1.25 for children; tennis is $2 an hour for a court; guided trail riding is $8 an hour; rowboats rent for $2 an hour and paddle boats for $3 an hour, $2 for half an hour. Greens fees on holidays and weekends are $13.50 for 18 holes, $8.50 for nine; and on weekdays, $12 for 18, $7.50 for nine.

Here's a sampling of some of the lodging prices. Cabins built for four range from $250 to $320 for a week, the minimum period during the summer. After Labor Day, you can rent cabins by the day (from $45 to $69 for a foursome) except on weekends when the minimum rental is two nights. In summer, single rooms at the lodge are $32, doubles $37. Winter rates are $23 and $28. Additional people in a room are $4 each except for children under 13 who can stay free in a room with their parents.

HOW TO RESERVE -- Reservations for rooms and cabins at Cacapon State Park can be made through a toll-free number, 1/800/624-8632, from 8:30 a.m. until 4:30 p.m., Monday through Friday, except on holidays. Pets are allowed in the park, on a leash, but not permitted in the lodge.

GETTING THERE -- From the Beltway in Maryland: Take I-270 north to Frederick, I-70-40 west to Hancock, Route 522 south through Berkeley Springs to the park. From the Beltway in Virginia: Take U.S. 50 or Route 7 west to Winchester, then Route 522 north to the park. MORE TO GO FOR

Another of West Virginia's state parks a short drive from Washington is Lost River, near Mathias. The park area covers 3,712 acres and includes hiking trails, tennis courts, horse stables, picnic areas and swimming. There are 24 rental cabins.

For information on any of the state's park facilities, write: West Virginia Department of Natural Resources, Division of Parks and Recreation, State Capitol-SP, Charleston, W.Va. 25305. Or call 304/348-2764.