There may be no better family holiday than a week at a ski resort.

Skiing, after all, is one of those rare popular sports in which grown-ups don't hold all the advantages. When the youngsters get their downhill legs (a season or two of lessons may be all it takes), they manage to keep up with no trouble at all. And soon enough, it's Mom and Dad who are the stragglers.

This is the kind of vacation where families can spend as much time together as they want, but get away from each other for a while, too. Individuals can join a ski class or group, according to ability, and then meet later for a few last runs together at the end of the day.

Skiing carries a lingering reputation as the wintertime frolic of the well-heeled singles set, who rank lively apre s-ski quite as high as the quality of the slopes. But many ski resorts, among them some of the best in the country, are shunning that image to attract families.

"We're not into a lot of swinging night spots," says Lillian Ross, a spokeswoman for Keystone Resort, a major ski mountain in Colorado that enjoys its reputation as a family resort.

In fact, the ski industry sees the family as an increasingly significant market.

"Postwar baby boomers are starting their own families now," says Cal Conniff, president of the National Ski Areas Association, which represents 400 U.S. ski mountains. "They were the kids who fueled the growth of skiing when they were young."

To keep drawing these skiers, resort managers realize they are going to have to welcome their new offspring, too. This winter, predicts Conniff, ski areas will make a "big boost" in programs and facilities for families.

Among the friendly extras:

*At Smugglers' Notch in northern Vermont, ski school instructors light an outdoor bonfire every afternoon. Families gather around it after the last run down the mountain for a warming cup of cider or chocolate. It's cozy and it's fun, for both kids and parents.

*Youngsters at Big Sky of Montana, the resort founded by TV anchorman Chet Huntley 10 years ago, are invited to attend the weekly movie night at the lodge, complete with popcorn and pizza.

*At Keystone, teens can meet friends at the Breakaway pizza arcade and teen center, a lively spot filled with electronic games, pinball machines and jukeboxes.

True, no week at a major U.S. resort in New England or out west comes cheaply. Skiing is expensive when the cost of lift tickets, lessons and equipment is added to such basics as transportation, lodging and meals. When a family of four travels, the total multiplies rapidly.

Recognizing the problem, resorts are attempting to make things easier on the family budget by offering special packages or discounts. In many places, no charge is made for children 12 or under who share a hotel room or condominium with their parents. At Steamboat Springs in northern Colorado, preteens also can ski free when their parents buy a five-day lift ticket.

A very important factor, especially for couples with younger children, is a resort's day-care and ski school facilities and evening baby sitters.

California's Northstar-at-Tahoe is among the three dozen resorts offering SKIwee, a national program of ski lessons for ages 5 to 12. Instruction is designed specifically for children (no baffling terminology), and the emphasis is on having fun while learning. Young skiers spend the full day with the class, and supervision continues even through the lunch break; the cost is $40 a day.

Northstar's Peewee program takes tots as young as 2 years for a full day's activities that include crafts, storytelling and outdoor play in the snow. At age 3, they can begin ski classes with a daily 90-minute lesson. The Peewee price, including a hot lunch and two snacks, is $27 a day; ski lessons are $5 extra.

Such programs can be fun for the youngsters while freeing their parents from child-care responsibilities for part of each day or week. As Dorothy Jordan, editor of "Family Travel Times," a newsletter of tips on traveling with children, points out: "It's not a vacation if you have to spend all your time with your children."

To which a child might add, "or with your parents."

Here's an across-the-country sampler of excellent, full-service resorts that cater to skiing families:

*Smugglers' Notch, Vt.: Take a scoop of fresh snow, pour maple sugar over it and you have a traditional New England treat, an authentic snow cone. They serve them up frequently at "sugar and snow" parties in this northern Vermont resort.

It's a taste of the family fun atmosphere that Smugglers' Notch has created at the foot of three interconnected mountains: bump-filled Madonna for experts; gladed Sterling for intermediates; and gentle Morse for beginners. One night a week, the instructors stage a torchlight parade, gliding down the slopes in a dance of fire.

But Smugglers', a self-contained village where all the condominium lodging is conveniently located within 250 yards of the lifts, also welcomes families with a number of bargain packages.

On most five-day ski packages this season, children ages 3 to 14 can enroll in the Discovery Ski Camp. It includes morning and afternoon lessons, lunch, crafts and other play activities for younger participants at a five-day cost of $85 for ages 3 to 6 and $90 for ages 7 to 14.

All this is free, however, for children 12 and under during five Family Fest weeks: Dec. 16-21 and 21-26; Jan. 20-25; Feb. 3-8 and March 17-22. Additionally, rental equipment is free for ages 12 and under during Family Fest, and so is evening dinner when the youngsters eat with their parents at the Village Barn.

A typical five-day Club Smugglers' family plan for four (children 12 and under) begins at $845 (Sunday through Thursday) in a "deluxe studio" and $1,025 in a one-bedroom suite. The cost includes a five-day ski pass, five lessons per person, a visit to the Scandinavian hot-tub and sauna spa and a prime-rib dinner party with the instructors.

Even a nonskier might find plenty to do in a day's activities that include outdoor ice skating, sledding, horse-drawn sleigh rides, indoor tennis, evening movies on big-screen TV and an after-hours "splash party" in the heated pool.

Smugglers' Notch, Vt. 05464, (802) 644-8851. About 28 miles east of the Burlington airport, and a bit closer to the Amtrak station at Essex Junction. Transfers can be arranged at $12 each way, ages 12 and under free.

*Keystone Resort, Colo.: A visit to Keystone in central Colorado should convince doubters that a self-professed "family resort" can provide even expert skiers with the thrill of downhill challenges. This season, Keystone is opening its mostly expert North Peak area, 15 steep trails served by six-passenger gondolas climbing above 11,000 feet.

But the large, attractive resort also has a fine mix of beginner and intermediate slopes, all convenient to the condominium lodging. And all of the condos have indoor or outdoor heated pools or both.

Much of Keystone is set around a charming lake, where ice-skating under the stars is a popular evening's entertainment. Lighted trees, the colors reflected by the frozen surface, cast a warm glow that belies the night's chill.

At Keystone, children 12 and under stay free with their parents: parents in the bedroom, children on a sleep sofa in the living room. Low-season rates for a seven-night, six-day lodging and lift-ticket package begin at $1,038 for a family of four (children 12 and under). Low season is now until Dec. 21; Jan. 6 to Feb. 7 and April 8-21.

The nursery takes children as young as 2 months ($30 a day). At age 3, they can be enrolled in a "Mini-Minors Camp," where they are given indoor and outdoor play activities (all-day cost, including lunch, $35). At 4, they can begin ski lessons (all day, lunch and lift tickets included, $35 a day; less for multiple days).

One night, plan a valley sleigh ride to Soda Creek Homestead for a festive steak dinner. It's a treat for the whole family.

Box 38, Keystone, Colo. 80435, (303) 468-4242. Located 75 miles west of Denver on I-70. Bus and shuttle service available.

*Big Sky of Montana, Mont.: It sounds remote, but like most of these resorts, Big Sky is convenient to an airport (43 miles south of Bozeman's), and you don't need a car to get to or around the resort. At Bozeman, shuttle buses meet the plane for an hour's drive through beautiful winter-draped Gallatin Canyon.

The resort is small, quiet and relaxed. The lodge and condominiums sit at the foot of 11,166-foot Lone Mountain, and the ride up is on two gondolas and four chair lifts. Experts can try helicopter skiing in high powder bowls.

Ski school for the youngsters begins at age 6. It is an all-day program that includes morning lessons, lunch at the cafeteria and a varied afternoon of ice skating, swimming in the outdoor heated pool and crafts and games ($23 a day). Minimum age at the nursery is 1 year, and there is a full day of indoor and outdoor play activity ($22 a day).

Here, too, children 12 and under stay free. The seven-night, six-day low-season rate for a one-bedroom condo for a family of four (two children 12 and under) begins at $974, including lift tickets. Low season is Nov. 21 to Dec. 25; Jan. 2-24 and April 14 to closing.

Take a day off from skiing for a snowmobile or snowcoach tour of the bubbling geyser valleys of Yellowstone National Park, just 18 miles south of Big Sky.

P.O. Box 1, Big Sky, Mont. 59716, (800) 548-4486. Shuttle buses are $13 round trip from Bozeman's airport.

*Snowbird, Utah: "The greatest snow on earth," boasts Snowbird, one of the country's major resorts in the Wasatch Mountains just outside Salt Lake City. And it's no idle claim. Snowbird averages about 500 inches of snow every year.

The terrain is vast and the lift system is extensive, including a 125-passenger aerial tram that climbs to the 11,000-foot summit of Hidden Peak. And yet, for all its big-time glamor, this remains a fine family resort.

Don't let the size frighten you. Snowbird introduces skiers to its slopes in a quite hospitable way. Guests with lift tickets are treated to a two-hour skiing tour of the mountain. A guide skis with each family, judging their ability and pointing out what trails they might enjoy most. The guides are available at 10 a.m. or 1 p.m. daily at the Snowbird plaza.

Nightlife at Snowbird is lively but not frantic, and the youngsters are not forgotten: bars and dancing apre s-ski for the adults; for the kids (and parents, too), ski movie nights, an adventure lecture series and a welcoming outdoor heated pool.

Day-care for children age 3 and older (and out of diapers) is free from 9 a.m. to 4:30 p.m., although parents must pick up the youngsters for lunch. A Kinderbird ski school program begins at age 4 1/2, with an hour of lessons morning and afternoon, other supervised play and lunch for $32 a day. From ages 6 to 12, there are two hours of lessons morning and afternoon along with lunch and other sports activities, also for $32 a day. Older children may need to buy a lift ticket.

Children 12 and under stay free. A seven-night, six-day package for two adults in a "loft-suite" (room for two children) begins at $1,810, including two adult lift tickets. The price for a family of four (two children over 12) begins at $2,152, including four lift tickets.

The rates drop substantially between April 6 and May 5. Even that late in the season, there's still plenty of snow.

Snowbird, Utah 84092, (800) 453-3000. Located 31 miles from Salt Lake City airport. City bus, taxi and shuttle bus service available.

*Northstar-at-Tahoe, Calif.: Northstar prides itself on the intimate flavor of its small village at the base of 8,600-foot Mt. Pluto in the Sierra Nevada Mountains. Unlike other nearby Lake Tahoe resorts, Northstar is self-contained, with slopes convenient to the condo accommodations.

While the youngsters tackle the slopes in Northstar's SKIwee program, their parents can sample the trails at nearby Alpine Meadows and Squaw Valley (or even the Tahoe casinos just across the state line in Nevada).

A one-bedroom condo (with pullout couches for the kids) rents for $848 for a family of four on a seven-night, six-day package, including lift tickets.

Saunas and outdoor hot tubs at the Recreation Center soothe tired muscles, and movies -- old westerns, appropriately -- are shown after dinner.

P.O. Box 2499, Truckee, Calif. 95734, (800) 824-8516. Located 40 miles west of Reno's airport. The resort advises renting a car, which then is handy for visits to other resorts and the casinos.