Skiing is expensive, no doubt about it, especially when the whole family wants to go along. A skier's vacation budget must cover transportation, lodging, food and the cost of a daily lift ticket -- often $20 or more.

Skiers (downhill and cross-country) who take the time to shop around, however, will find attractive bargains to cut their costs. And this winter, resorts also are offering some unusual incentives to attract new skiers and keep longtime enthusiasts.

The latter know that the least expensive time to ski is during the "low season," when many resorts -- including those in the mid-Atlantic region, New England, the Rockies and Sierras -- offer reduced rates for lodging and lift tickets. Another advantage is that lift lines are shorter, so skiers get more runs down the mountain for their money.

Low season varies among resorts, but generally it extends from the end of the Christmas-New Year holiday through January and again from the end of March into April, when most resorts close. Another low period is from opening day (around Thanksgiving) until mid-December and the start of the holiday rush -- too late for this winter but something to consider for next year.

Midweek is also a bargain time. Resorts that depend on large weekend crowds from the big cities -- particularly those close to Washington and in New England -- frequently cut rates for Monday-to-Friday skiers. And the midweek slopes, like those during low season, are less crowded.

Competition for skiers is keen, so individual resorts are offering a variety of special bargains -- and other interesting packages -- to lure skiers of all ages and abilities. Among the programs available this winter:

*For beginners: The quickest and safest way to learn to ski is to take lessons from a certified instructor. Reckless beginners can be a threat not only to themselves but to more experienced skiers on the slopes. At least two resorts are making an effort to introduce novices to the sport inexpensively -- and safely.

First-time skiers are given a free 90-minute group lesson at Wintergreen resort in Virginia's Blue Ridge Mountains southwest of Charlottesville. To qualify, the beginners must rent equipment -- skis, boots and poles -- at Wintergreen. The standard rate for a group lesson is $11. Last season, 12,000 new skiers took the free lesson. For more information: (804) 325-2200.

Out West, a similar "Start 'Em Off Right" free half-day lesson for "never-ever" skiers is featured at Purgatory, a growing resort in the high Colorado Rockies near Durango. The regular price for a group lesson at Purgatory is $20. For more information: (800) 525-0892. For families: Many families may want to ski during the low season, but they are hesitant to take their children out of school -- school holidays generally fall during high season. Bolton Valley, a family ski resort in northern Vermont, has an answer: the Bolton Mountain School.

The school is a Monday-through-Thursday study hall under the supervision of a Vermont state-certified teacher. It opens after the day's skiing is over, from 4:30 to 6 p.m. Students -- grades 1 through 8 only -- must bring a written program of study from their regular teacher, along with their books, pencils and paper.

The Bolton teacher makes sure the homework is completed and can offer assistance if needed. The study room is equipped with a blackboard, desks and chairs. The weekly rate is $25 for the first child and $12 for each additional child. For more information: (802) 434-2131.

Elsewhere, Aspen Highlands, a super resort for all abilities in the famed Colorado resort town of Aspen, features a "Family Plan" lift ticket that is especially advantageous to large families. It is a one-price ticket for the whole family -- both parents and all children ages 18 and under.

The regular rate for one day of skiing at the Highlands is $26 per person. Under the Family Plan, the price per family is only $60 for one day, and the rate gets cheaper the more days a family skis: two days, $110; three days, $150; six days, $264. For a family of six on a six-day holiday, that figures out to $7.33 per person a day for lift tickets. For more information: (303) 925-9000.

Closer to home, Canaan Valley Resort State Park near Davis, W.Va., is offering a midweek "Kids Love Canaan" package. Parents pay the resort's regular rate of $228 for three nights' lodging and three days' skiing. But one or two children 12 and under, sharing the room, can stay at no extra cost.

In addition, the youngsters get free lift tickets, equipment rental and a daily hour-long lesson. A midweek lift ticket alone is $14 per person a day. Accommodations are in the resort's modern motel-like lodge, and each room has two double beds. For more information: (304) 866-4121. For adventurers: The lure is deep-powder skiing away from the bustle of a crowded resort. The destination is the high wilderness of Canada's Selkirk Mountains in British Columbia, about 250 miles north of Spokane, Wash. The Selkirks average 400 inches of snow each winter.

For a decade, Selkirk Wilderness Skiing Ltd. of Meadow Creek, B.C., has been offering snowcat skiing for small groups of vacationers who come for a week at the ranch-style lodge. The heated snowcat holds 12 passengers, who are carried to the top of Meadow Mountain at 8,100 feet for five days of skiing. The runs -- through woodlands or across open bowls -- range from two to 10 miles in length.

Most groups make about eight runs a day, with the pace set by each week's participants. The program caters to "strong intermediate skiers," with instruction provided for those without deep-powder experience.

Snowcat skiing is much like heli-skiing, where helicopters carry skiers to the mountaintop -- quite popular with seasoned skiers. But snowcats are not grounded by bad weather, and the price is lower.

The charge for a week in the Selkirks ranges from $1,060 (low season) to $1,410 (high) per person and includes six nights' lodging, all meals, five days of guided skiing and round-trip transportation from Nelson, B.C. For more information: (604) 366-4424.

*For couples: It is a fact of life that couples traveling without children can often afford more comfortable accommodations. Still, there's no reason to pay more than necessary. The Mark, a large Marriott resort hotel in Vail, the plush Rocky Mountain ski area outside Denver, is offering a low-season "Vail Escape Package" for two at considerable savings.

Dubbed "Hit the Mark," the package provides a deluxe hotel room -- mountain view, small refrigerator -- and two adult lift tickets for $130 a night. Also included is full use of the hotel's indoor pool, athletic room, hydrotherapy pools and saunas.

During Vail's high season a comparable room goes for $160 a night, and lift tickets are an additional $27 per person. The hotel is located within 200 yards of the Vail Mountain gondola in the heart of Vail. For more information: (800) 228-9290.

*For seniors: Up in Woodstock, a charming Vermont village, they figure -- not unreasonably -- that many vacationers in the 50-and-older crowd can't keep up with younger skiers and don't really want to try. So the Woodstock Inn & Resort has scheduled a series of three-day cross-country skiing packages designed for seniors only.

The package, "Seniors on Snow," includes daily lessons and guided tours that lead both from the Woodstock Ski Touring Center or the Village Green. The terrain is gentle -- open pastures and woodland trails -- and the pace leisurely. Participants can drop out for an afternoon's sightseeing or a good book beside the fireplace.

Weekend sessions are scheduled for Jan. 17-20 and March 14-17 at $280 per person (double occupancy). Midweek sessions are Feb. 9-12 and March 2-5 at $262 per person. Both rates include three nights' lodging in a deluxe room; breakfast and dinner daily; instruction and tours; use of equipment; and a welcome reception. For more information: (802) 457-1100.

*For the "frequent skier": The airlines honor frequent fliers with free airline tickets. Mount Snow, one of Vermont's largest and most famous resorts, is awarding free lift tickets to frequent midweek skiers. Mount Snow claims its "Frequent Skier Program" is the first in the country.

Under a not-too-complicated system, skiers earn points for every midweek lift ticket they purchase: two points for a ticket bought either on Monday or Friday; three points for a Tuesday, Wednesday or Thursday ticket; one point for a group lesson. Twelve points earn a free midweek ticket; six more points earn a second free ticket; and each additional three points earn another free ticket (or one free ticket for every Tuesday-through-Thursday ticket purchased).

The savings can mount up. A single midweek ticket at Mount Snow is $26. The program is available throughout this year's ski season. For more information: (802) 464-3333.

These programs are only samples of what is available at many ski resorts. To find out about other packages, consult: The individual resort.

*The tourism office in the capital of the state you are interested in visiting. Ask for information about special family or bargain vacation packages.

*A good travel agency, particularly one specializing in skiing vacations.

*Resort brochures often available at ski sales and rental shops in the Washington area.

*One or more of the monthly skiing magazines, available at many news counters. COSTLY BARGAINS:

Not everything that looks like a travel bargain really is -- so be sure you know what you are getting, warns the American Society of Travel Agents.

Obvious advice, perhaps, but it comes as a result of promotional offers being made around the country that, for example, promise a vacation trip for two people to an exotic destination for the price of an airline ticket for only one person. It sounds good, but it may not be the big bargain you were expecting.

These offers frequently are made as an incentive to get you to buy something expensive, perhaps a car or furniture, or they are awarded as a prize. But check the fine print carefully, says Ray M. Greenly, ASTA's consumer affairs director, because there may be a catch.

To qualify, one of the travelers typically is required to buy an unrestricted full-fare round-trip ticket to obtain the so-called free vacation for a companion. But these full-fare tickets, Greenly points out, are considerably more expensive than the advance-purchase discounted fares available to vacationers on most airlines.

In one promotion cited by ASTA, new-car shoppers recently were offered a free trip to Hawaii for two, including seven nights' lodging, if they purchased what was specified as a "standard Y-class" round-trip ticket. The current price of such a ticket between Washington and Hawaii, quoted by a major airline, is $1,516.

However, the same airline also is offering a 14-day advance-purchase ticket that ranges from $549 to $689 per person, depending on the date of travel. And local travel agencies can offer one-week vacation packages on Waikiki Beach -- air fare from Washington and a choice of hotels included -- beginning at only $614 per person or $1,228 for two.

This means the car-shoppers could have taken a trip to Hawaii on their own for much cheaper than what was provided by the promotional offer -- and they wouldn't have had to buy a car.

In the past half year, Greenly's office has gotten "several hundred" inquiries from throughout the country from callers who want to know if such incentive offers are valid bargains. He advises the callers to determine what the promotional vacation will actually cost and then do comparison shopping to see if they can get a better deal elsewhere. CASTLES IN WALES:

It's a new day and a new life for the ancient castles of Wales, all 127 of them open to the public. An organization called Cadw Welsh Historic Monuments recently has been formed with the aim of enhancing visitor enjoyment and appreciation of these splendid structures.

Cadw is a Welsh word meaning "keep," as in preserving. The pronunciation is something like "ka-DOO."

Among the new developments for 1986: the introduction of guided tours at major castles; a lively program of appropriate events, including concerts, jousting tournaments and medieval fairs from April through September; exhibits to explain the history of the castles and the daily life of their residents; attractive new guidebooks; and improved road signs to aid visitors in finding their way to these historic sites.

Additionally, Cadw is promoting a lodging and meals program called "Stay Close to a Castle." There are two-, four- and six-day packages at a choice of 42 selected hotels, inns or guest houses with a view of a castle or within walking distance of one.

For example: At spectacular Harlech Castle, a mammoth rock-walled fortress from the 13th century that occupies a high hilltop setting on Tremadog Bay in North Wales, a visitor can stay at the Rum Hole Hotel, an eight-bedroom establishment described as "nestling under the castle walls."

The winter rate for a two-night stay, from now through April 30, is about $47 per person (depending on the exchange rate), including breakfast and dinner both days. Summer rates for the same package (May 1 through Sept. 30) are about $5 more per person. Winter rates for similar two-night stays at other hotels in the program range from about $36 to $112 per person.

For more information on travel in Wales: British Tourist Authority, 40 W. 57th St., New York, N.Y. 10019, (212) 481-4700 or the BTA's British Travel Centre at the Old Post Office Pavilion on Pennsylvania Avenue NW. For information on "Stay Close to a Castle" packages: Consult a travel agent or write City Travel Limited, 13 Duke St., Cardiff, CF1 2AY, Wales, Great Britain.