There are those who say this isn't a skier's town. So why does almost every local recreation department sponsor ski trips? You can't get any more public support for a sport than to have the local government promote it.

The recreation departments in the District and Arlington, Montgomery and Prince George's counties, to name the nearest ones, sponsor one-day and weekend trips to local ski areas. They rent the bus, get group rates for lift tickets, lessons and equipment rentals (and hotels, where necessary) and pass the savings on to you. You don't even have to live in the government jurisdiction to get in on these trips - which is handy for people from Fairfax County and Alexandria, where such trips aren't sponsored.

Not all dates and prices have been set, but for your planning, here are the latest details: DISTRICT OF COLUMBIA

The Recreation Department's Neighborhood Planning Council hopes to offer free ski trips to youths between 13 and 21. The first trip, probably to Ski Roundtop, will be Feb. 11, leaving from the NPC office, 4025 Chesapeake St. NW.If the trip is successful, another may be planned for March. Tony Murdock, NPC director, said that if he can't make the trip free, he'll try to keep the cost down to $5 for transportation. Lift tickets and rentals are not included. To sign up, go to the NPC office. For more information, call 244-7774. ARLINGTON COUNTY

Arlington's Recreation Department features both downhill and cross-country skiing. Downhill trips include:

Saturday, Jan. 14 - Ski Roundtop. Leaving Dawson Terrace Community Center, 2133 N. Taft St., at 8 a.m. $15 for transportation and lift tickets; $8 for rental equipment. To register, call 558-2700; after Jan. 3, call Michael Ingram, 558-2270.

Wednesday, Jan. 25 - Ski Roundtop. Leaving Dawson Terrace Community Center at 4 p.m., returning at midnight. $12 for transportation and lift ticket; $5 for rental equipment. Call 558-2700; after Jan. 3, call Michael Ingram, 558-2270.

Weekend of Jan 19-22, Southern Highlands, N.C. Leaving Kenmore Junior High parking lot, 200 S. Carlin Spring Rd. at 11 p.m. Transportation, two nights lodging - four to a room, two days lift passes, two breakfasts, one dinner. $95. Deadline Jan. 6. Call Jackie Abrecht, 558-2154.

Weekend of Feb. 10-12 - Seven Springs. Leaving Dawson Terrace Community Center at 6:30 p.m. Feb. 10. Transportation, two nights lodging, lifts, two breakfasts, one dinner. $62 for three in a room. Call 558-2700; after Jan. 3, call Michael Ingram, 558-2270.

Weekend of Feb 24-26, Seven Springs, Pa. Leaving Lubber Run recreation center, 300 N. Park Dr., 3:30 p.m. Transportation, two nights lodging - four to a room, two days and night of lift passes, two breakfast, one dinner, unlimited use of heated swimming pool. $69. Deadline Feb. 4. Call Jackie Acrecht, 558-2154.

Three cross-country skiing trips are scheduled for Jan. 22, Jan. 28 and Feb. 4. Details will be available in January from Ann Suter in the Arlington Recreation Department, 558-2867. Cost estimated to be $11 to $15, including transportation, trail lunch and basic instruction. Destination will depend on snow condition. MONTGOMERY COUNTY

Montgomery County's Recreation Department plans eight trips, all on Sundays and all leaving from the Cubin John Shopping Center at Seven Locks and Tuckerman Road, Potomac.

Jan. 8 - Blue Knob. $19 bus and lift ticket; rentals $7.50, lesson $4.50. Leaves 6 a.m.

Jan. 15 - Wintergreen. $20 bus and lift ticket; rentals $8 lessons $6. Leaves 6 a.m.

Jan. 22 - Hidden Valley. $20 bus and lift ticket; rentals $7, lessons $4. Leaves 5:30 a.m.

Jan. 29 - Bryce Mountain. $20 bus and lift ticket; rentals $9, lessons $6. Leaves 6:30 a.m.

Feb. 5 - Wisp. $19 bus and lift ticket; rentals $9.50. Lessons $6. Leaves 5 a.m.

Feb 12 - Massanutten. $20 bus and lift ticket; rentals $9, lessons $7. Leaves 6 a.m.

Feb 19 - Ski Liberty. $16 bus and lift ticket; rentals $8, lessons $5. Leaves 6:30 a.m.

Feb. 26 - Ski Roundtop. $18 bus and lift ticket; rentals $8, lessons $5. Leaves 6 a.m.

There may be ski trips in March, too, depending on the weather. Sign-up deadline is Friday noon before each trip. For registration forms to be mailed to you, call 468-4217.

Montgomery County also offers ski lesson packages. You get five lessons at Ski Liberty, round-trip transporatation, equipment and lift tickets for $85. The lesson series stating Jan. 4 runs five consecutive Wednesday nights; bus leaves Quince Orchard shopping center 5:45 p.m., and returns midnight. For lessons beginning Jan. 6 for five consecutive Friday nights, bus leaves Cabin John shopping center 5:30 p.m., returning midnight. Children under 10 must be accompanied by a parent, older relative or guardian. No children under 7. For more information, and to have registration form mailed, call 468-4217. PRINCE GEORGE'S COUNTY

Prince George's Recreation Department has six trips lined up that are not filled yet. All but one are day trips. To get more information, or to register, call 277-2200, ext. 369.

Jan. 13 - Ski Liberty. Leaving Marlow Height Shopping Center on St. Barnabas Road at 7.30 a.m., bus goes on to the Park and Planning Building, 6600 Kenilworth Ave., Riverdale, and departs there at 8 a.m. $14 for transportation and lift ticket, $7 for rental equipment and $5 for a group lesson. Registration deadline Dec. 30.

Jan. 27 - Blue Knob. Leaving Marlow Heights at 6:30 a.m. and the park and Planning building at 7 a.m. $16 for transportation and lift ticket; $6 for rental equipment; $3 for a group lesson. Deadline Jan. 13.

Feb. 1 - Ski Roundtop. Leaving Marlow Heights at 7 a.m.; the Park and Planning Building 7:30. $15 for transportation and lift ticket; $7 for rental equipment, $5 for a group lesson. Deadline Jan. 13.

Feb. 3 - Ski Liberty night skiing.Leaving Marlow Heights at 5 p.m.; the Park and Planning building, 5:30. $12 for transportation and lift ticket, $5 for rental equipment and $5 for a group lesson. Deadline Jan. 20.

Feb. 20 - Ski Roundtop. Same as Feb. 1 except transportation and lift ticket is $18, rental equipment is $8. Deadline Feb. 3.

Weekend of Jan. 19-22 - Hunter Mountain. Transportation, three nights in a hotel, transfers to ski area, a pizza party and a wine and cheese party, six meals, a discotheque and live entertainment. $96 for four in a room, $105 for three in a room, and $119 for a two in a room. Extra fee for lifts ($8-12) and rentals ($8). Deadline Jan. 6.

Prince George's includes lessons in the package for an additional fee in the belief that all beginners need them, both for safety and for fun.