Mountains of Family Ski Programs : About 500 children a day enroll in skiing sessions at one major resort. Another offers money back if children don’t have fun.

“You’re skiing much better now, Mom,” 6-year-old Reggie shouted in support of my efforts as she raced past me down the mountain. “Come on the bumps with us,” urged 8-year-old Matt as he also sped by.

After two days of ski school, Matt and Reggie were brimming with confidence navigating the moguls on the intermediate trails, certain they could ski any terrain, arguing over who was the better skier as they rode the gondola to the summit.

Virtually all major ski resorts, from Vermont to New Mexico to Utah, have been working hard lately to attract families by offering ever-expanding day care and specialized programs to teach children and teen-agers to ski. We were spending a long President’s Day weekend at Keystone Resort, just 75 miles from Denver and one of the country’s premier family ski areas. But we could just as well have been at Snowbird or Park City, Utah, or at Smugglers’ Notch in Vermont, since all are known for catering to families.

Many areas want family business so much that, like Steamboat Springs, Colo.; Red River, N.M.; Snowbird, Utah, and Mt. Snow, Vt., they now offer “kids-ski-free” deals for much of the season. Even Aspen/Snowmass offers kids-ski-free deals for children under 6.

Twice winner of Family Circle magazine’s Family Resort of the Year award, Keystone, owned by the Ralston Purina Co., strives to accommodate families--from the first-rate children’s ski program (a child psychologist advises the instructors on how best to motivate the 40,000 kids who ski here each season); to the nation’s largest night-skiing program (let the teen-agers ski until 10 p.m. while you relax in the hot tub); to evening children’s activities (the condo came equipped with VCR and kids’ videos), to the professionally run day-care center where infants are welcome. (Nervous parents can check out a beeper to stay in touch while skiing.)

It’s best to call the ski schools before booking and ask what kind of programs and special packages they offer. Other questions you should ask: Have the instructors had special training for teaching kids? How many children are there per instructor? Are there apres- ski children’s activities so that parents can have time to themselves in the evening? Make sure day care is available for children under 3 who typically are too young to ski, and ask if it’s necessary to reserve a slot ahead of time.

A growing number of ski areas--Keystone and Beaver Creek, Colo., among them--now have exclusive kids-only ski areas. At Beaver Creek, an upscale resort known for its commitment to family skiing, costumed storytellers are on the mountain to amuse children with tales of the Old West.

In keeping with the spirit of vacations that involve no-hassle planning, I booked our family ski trip last fall with one call to Keystone (800-222-0188). That call resulted in flight reservations, car rental, lodging, lift tickets--even dinner reservations and baby-sitting. (Five-night, four-day packages start at $749 a person from Los Angeles with four people sharing a condominium; the price will drop in April.)

The snow conditions were the best in years and the place was packed with families from across the country, even though gay and lesbian groups had called a boycott of Colorado tourism to protest what they view as discriminatory legislation passed by voters last November. (A Denver judge has since suspended the measure pending the outcome of a court challenge.)

Some 500 kids a day were enrolled at the Children’s Ski School while we were there.

Despite our late arrival the night before, the kids were ready to go in time to get to ski school at 9 a.m. They dressed in layers, from long underwear and ski socks to turtlenecks and sweat shirts, waterproof snowsuits and gloves and wool hats, and complained bitterly about all the paraphernalia. But they grudgingly donned their goggles and smeared SPF 15 (or higher) sun block on their faces (the sun’s ultraviolet rays are strong and can be damaging at high altitude).

Keystone makes it easy for families, although it is expensive. We checked the children into ski school ($60 a day per child pays for lift tickets, lessons, equipment rental, snacks, lunch and after-ski care, though we, like most parents, returned when the children’s lessons were over at 2:30 p.m. to get in some family ski time).

And I was pleased that despite the crowd, the ratio of instructors to children was high: four preschoolers to one teacher; no more than eight older children to one. At the end of the day, they gave us a blue “report card” charting the kids’ progress.

While few parents are equipped to teach their kids to ski, experts say a good strategy is to alternate lessons with family ski time. “That is, if your kids want to be with you,” joked Deb Rosenberg, the Denver child psychologist who works with Keystone’s instructors.

Rosenberg advises parents to prepare kids for what to expect on a ski vacation. Show younger kids pictures; study the trail map with older children. Even older kids may be uneasy in a new environment. If your kids are small, you don’t want to make a bustling ski area their first day-care experience. Don’t forget to tell them when you’ll be back.

And be careful what you eat and when you eat it. One day when we picked up Reggie and Matt for lunch, we paid nearly $50 for the four of us. Next time, I’ll take my cue from a family from Boulder, Colo., who shared our table. They brown-bagged it, stowing their sandwiches and oranges in a locker at the summit.

(For more information on family skiing in Snowbird, Utah, call 800-453-3000; Park City, Utah, 800-222-PARK; Smugglers’ Notch in Vermont, 800-451-8752; Aspen/Snowmass, Colo., 800-26ASPEN or 800-525-6200; Beaver Creek, Colo., 800-622-3131.)

Taking the Kids invites reader questions and comments about family travel. Address them to: Taking the Kids, 2859 Central St., Box 119, Evanston, Ill. 60201.