(MONEY Magazine) – Now that so many formerly swinging-single skiers have transformed themselves into upscale moms and dads, the nation's winter resorts are getting family- minded too. Of 650 or so ski areas in 40 states, from Stowe, Vt. to Sun Valley, Idaho, some 600 offer family facilities. Many bill themselves as child-centered, with special programs for preschoolers, babysitters at night and plenteous activities for youngsters on and off the slopes. All told, ski resorts expect to serve more than 3 million families this winter. To get their share of this growing crowd, resorts are packaging deals at attractive prices. Ordinarily, the tab for a week for a family of four at a major resort such as Vail, Colo. can go as high as $2,000. Yet you can get away over the weekend at some worthy slopes for $600 or for five midweek days before or after the height of the season for under $1,000, including rental equipment, lift tickets, instruction and child care -- just about everything except food and transportation. But watch out for snow jobs. At a small ski area near Lake Tahoe, Calif. last February, Ron Phillips, 48, of Los Angeles rented equipment and arranged a private lesson for himself, his wife Linda and son Kenyon, 9, all first-time skiers. Because the beginner's slope had no lift, however, the family had to trudge up it on their skis again and again. Worn out and discouraged after two hours, they quit and spent the afternoon making a snowman. Fortunately, the next day they found a better-equipped area just a few miles away. After a morning of lessons on novice slopes served by easy-to-use lifts, they found themselves whooping down the hills together. Finding the right place for your household takes finicky attention to details unmentioned in glossy brochures. Make a bad choice and your kids will be miserable. So will you. ''You can be sure that parents won't enjoy themselves unless the kids have a good time,'' says Hank Thiess, director of the ski school at Keystone Mountain in Colorado. With some advance scouting you can find true family ski resorts that offer packagepriced holidays at your choice of economy or luxury levels. Not many places have gone so far as to turn their ski instructors into social directors. But resorts such as those in the table at left are moving in the right direction to meet the needs of young children. The most conspicuous change is the emergence of full-scale programs at which kids from three to 12 check in after breakfast and don't leave until the lifts close around 4 p.m. During the day they go outside for ski lessons or snow play and take lunch and naps indoors. Older children spend more of the day than younger ones on the slopes in the care of certified ski instructors. For infants and toddlers, some resorts have nurseries with cribs and play areas. One of the first to break out fresh trails for family skiing was the Village at Smugglers' Notch, a self-contained resort community in northern Vermont. ''Back around 1980 we noticed that the number of young singles, who were the bulk of our ski business, was declining,'' recalls Bradford Moore, the marketing vice president. ''So we concentrated on making this a place for the family.'' Many resorts that truly cater to families have lifts and beginner's slopes just for kids. And it is common courtesy for lift operators to reduce speed when beginners need help getting on or off.

The attitude of the ski instructors is even more important than facilities and programs. At some uncommendable schools, if an instructor is in the doghouse with the director, he gets stuck with teaching the children as punishment. ''That's entirely wrong,'' declares Christi Mueller Northrop, technical director of Skiwee, a 10-year-old, nationally franchised children's ski program. ''In Skiwee,'' she says, ''the teachers are there because they really like teaching kids.'' Her organization sets the standard for schools at 59 resorts in 26 states including Mammoth Mountain in the California Sierras, Solitude in Utah and Mount Snow in Vermont. ''The approach is really admirable,'' says Dorothy Jordon, whose company, Travel with Your Children, keeps files on more than 140 ski resorts in the U.S., Canada and Europe. ''Skiwee instructors talk to kids in language they understand.'' Other resorts have developed their own programs for kids. At Beaver Creek, Colo., part of the Vail complex, children have their own 150-yard ski run, Buckaroo Bowl. They learn the sport by whizzing down chutes, over tiny jumps and around playful obstacles such as snow castles and cartoon figures mounted on well-padded plywood. In the new pedagogical spirit, Beaver Creek instructors are never supposed to tell a kid that he is doing something wrong but only to show him better ways to maneuver. ''What is good technique for adults may not be right for a kid. What looks like just playing around can actually be a very effective method of learning,'' says John Alderson, who teaches there and has written books on training children to ski. At Snowmass, 12 miles from Aspen, the focus is on teenagers. Last year 5,723 youngsters schussed through the teen program there, up 20% from 1983. This year the same management is starting a teen program on Aspen Mountain. If not part of a package, all-day programs such as Skiwee and Buckaroo Bowl range from $25 to $60 a day, including lifts, lunch and ski equipment. Resorts with nurseries for infants and toddlers or licensed day care charge $20 to $40 a day. For a day's introductory skiing, you don't need a grand resort. The lift tickets and lessons at smaller areas with beginners' slopes may cost 30% to 50% less. You can get lots of information on individual resorts from Dorothy Jordon's series of fact sheets called Skiing with Children (Travel with Your Children, 80 Eighth Ave., New York, N.Y. 10011; $1 per report; minimum order $5). These reports describe skiing facilities, lodgings, restaurants, nursery accommodations, ski-school capabilities and prices. Another useful guide is $ The Book on Family Ski Vacations, available free from the Director of Public Relations at the Village at Smugglers' Notch (Rte. 108, Smugglers' Notch, Vt. 05464). The areas sampled in our table have Skiwee-like teaching programs, gentle slopes reserved for beginners, challenging terrain for experts and intermediates, and a variety of off-slope family activities. Dramatic savings are available if you can take advantage of heavily discounted midweek and off- season packages. Off-peak skiing provides another advantage: with fewer people on the slopes, you get more attention from instructors, and you avoid endless queues for everything from tickets to toilets. At Smugglers' Notch, for example, $974 buys a two-kid family five days of skiing, Monday through Friday, during eight of the 22 weeks in a typical Vermont ski season. The package includes lodging in a studio apartment, lifts, rental equipment, ski lessons, tennis, a spa, all-day children's ski camp and a prime-rib dinner for everybody. Unpackaged, the same vacation costs more than $1,600. Similar low-season family packages for around $1,000 are available at such outstanding resorts as Jackson Hole, Wyo., Whistler Mountain in British Columbia and Waterville Valley, N.H. Before you decide on a resort, try to get a recommendation from friends who have been there. Ask them how much attention the teachers paid to the kids. ''Watch out for instructors who are too cool,'' warns Keystone's Hank Thiess. ''If they spend a lot of class time talking with each other, they aren't really interested in their students.'' Don't hesitate to call the area's ski-school desk for information. Ask the following questions: What is the instructor-to-student ratio at the day-care center and the ski school? Indoors, says Dorothy Jordon, there should be one supervisor for every four kids under three and one for every six kids between three and five. On the slopes, the ratio should be one instructor for every five to seven kids. Is the day lodge at the base of the lifts centrally located? If all the ski runs arrive at the same main area, you are less likely to lose track of the kids. What activities does the resort have for bad weather and apres ski? Look for heated pools, indoor tennis and racquetball courts, skating rinks, game rooms and organized children's activities. Are reliable babysitters on call? This is a big plus. Can you reserve places for kids in the nursery and ski school? Resorts that operate on a first come, first served basis often run out of crib space and ski school room early. Does the resort have extensive snowmaking equipment? In the Rockies as well as the East and South, bare or icy slopes can mar your vacation. What is the cancellation and refund policy? Some places will refund lodging fees or reschedule dates if a warm spell washes out the vacation. Does the area provide enough challenge for members of the family who have mastered their downhill technique? No one likes boredom. Are there cross-country ski trails and is the proper equipment available for kids? Cross-country skiing is low in cost, easy to learn, and devoid of lift lines. Most of all, it goes well with a relaxed family vacation.

CHART: TEXT NOT AVAILABLE BOX: Resorts that cater to your kids Scores of family ski resorts run all-day programs for young children. This West-to-East sampling of five-day, midweek package prices includes lifts, lodging, equipment rental and daily ski lessons. Two rates are listed for a family of four with two children under 12 years old: first, an economy deal at low season in a simple inn with everyone staying in one room; second, a more luxurious setup with two rooms in a first-class lodge or hotel during high season. Canadian prices are in U.S. dollars. The people listed will give you details about children's programs and facilities.