Ski areas are doing their best to make skiing a family sport. There is hardly a ski area without a children's ski school, a nursery and a staff willing to warm up bottles or jerry-build a high chair out of pillows and a piece of rope if there is no high chair available.

However, as welcome as families are, not all ski areas have perfected their facilities for small and medium-size children. If you plan to take the kids with you when you go skiing for a day, a weekend or a week, you need to do your homework and prepare thoroughly for what you will find -- and not find. WHAT TO LOOK FOR:

A NURSERY. Whether or not your children ski, you will want them to have a place to spend several hours or the entire day while you get in a few more runs. While ski areas that don't have a nursery are happy to suggest a local resident who will take children for the day, or will recommend the names of people who will babysit for your kids in your motel or lodge room, you really don't want that. First of all, it puts the kids someplace far from where you are. Secondly, the kids would probably be happier staying home with a babysitter than traveling three or four hours to stay with a babysitter.

If the ski area has a nursery, you will need to know if the children will be fed lunch. If not, you will have to pick them up around noon and return them after they've eaten. In that case, you need to be sure that the nursery is in the base lodge, or close enough to it that the children will be able to walk to and from the cafeteria with you.

If you have an infant, make sure that the nursery will take the infant. Some won't because they don't have the facilities.

Be prepared to pay for the nursery; prices average $10 a day without lunch.

A BABYSITTER. If you plan to put the children to sleep in the room and go out to indulge in the apres ski life, you should confirm the services of a babysitter when you reserve your room. Babysitters are not readily available at ski areas, and the hotel or motel might have to stretch to find one.

EQUIPMENT. Most ski areas have rental equipment for children, but supplies may be limited. There's nothing worse than arriving at the rental shop ten minutes after the third and last pair of children's size 12 ski boots has been rented for the weekend. There are no substitutes for ski boots.

If you know your child's boot size, ask to reserve it ahead of time. If the area has night skiing, you might be able to rent equipment the night you arrive, saving yourself the early-morning trip to the rental shop to guarantee that you get the equipment you need.

LESSONS. Unless your children are old enough to ski with you or to ski by themselves, they will be happiest and safest in a class. The best classes are combined with children's programs that include lessons, supervised free skiing and rest periods. While these are expensive (ranging from $15 to $30 a session), they're worth the pleasure they give the children and the peace of mind they give you.

A GAME ROOM. That relaxing time just before or after dinner, when a beer or a brandy before a roaring fire is interrupted only by stories of the day's skiing, can be spoiled by a child's nagging. A game room is the answer. You can arm your youngster with a handful of quarters and tell him or her not to come back until it's time for dinner (or bed). In a pinch a television set can serve as a distraction as long as no adult changes from "Happy Days" to the evening news. WHAT TO BRING

WARM CLOTHING. Children need warm jackets, snowpants, hats and several pairs of mittens. They do not need ski pants, gloves or long underwear, unless you already have these items and want to use them.

The goal is to keep the children warm enough so they'll stay outside long enough to learn to enjoy skiing. Although children sometimes seem to have greater tolerance for cold (they make snowballs to throw at one another even when they're not wearing mittens), they have little patience for cold. When they have decided they've had enough, they want to go in. Immediately. Even if they have been outside only 15 minutes. So make sure they are warm.

Snow pants are necessary because they are warm (especially with a pair or regular pants underneath) and shed water. Nothing is worse for skiing than dungarees, which are not thick enough to keep out the wind and tend to absorb the melting snow picked up in the many falls children take. If your children don't have snow pants, borrow them or buy a pair. Don't buy ski pants, however: They're expensive, and no warmer than snow pants.

Several pair of mittens are a must. Mittens get wet and cold very fast on children, who find touching the snow fascinating. They also dry very slowly. So you'll want to be able to alternate them so the child always has a warm, dry pair. Mittens are much warmer than gloves. Adults wear gloves so they can adjust their ski boots and fasten their ski bindings with their gloves on. Children have adults to adjust and fasten, so do not need gloves.

If your child wears a scarf, it should be short, and should be tucked inside the jacket. A long dangling scarf can become caught in lifts, and poles, and under skis -- an invitation to injury.

FOOD. Ski areas offer food two ways: in cafeterias that specialize in hamburgers, hotdogs and fries, and in restaurants that specialize in drinks, hamburgers, hotdogs and fries. Rare is the ski area that serves peanut-butter sandwiches. If your children have a favorite food that's packable, bring it along. The choices at ski areas are limited, and you don't want to spend your day chasing down Hi-C or carrot sticks instead of skiing.

SPECIAL EQUIPMENT. There is no place to buy Pampers at a ski area.

GAMES AND BOOKS. Bring along a deck of cards for those times when the game room is not appropriate. And a few new books can be a welcome relief for the child who wants to escape the hubbub of the base lodge.

NECESSITIES. Each child should have in his pocket a packet of tissues and some lip balm. It's also a wise idea to tuck in a scrap of paper with his name, your name, your home address and phone number, and the name of the lodge at which you are staying.