Ask any hotelier restaurateur or shopkeeper in the Virgin Islands what kind of winter season he expects and 9 times out of 10 he'll grin and say, "Fantastic."

Two or three or four years ago the same person predictably would have glowered and responded, "Terrible."

The turnaround in this U.S. Carribbean territory's No. 1 industry - tourism - has far surpassed the expectations of the most optimistic business and government leaders who have worked hard to bring it about.

But on the negative side, a recurrent water shortage on St. Thomas and a sudden upsurge in robberies on St. Croix have made some tourism interests afraid of the possible repercussions.

Statistics tell the recovery story best, particularly for the hotels on the two major islands of St. Croix and St. Thomas.

On St. Croix, the largest of the three islands, the average hotel occupancy for the month of October 1973 was 13 per cent; in October 1977, it was 46.3 per cent. In November 1973, the average occupancy was 18.6 per cent; this year's November occupancy was 60 per cent. In each case there was a huge jump from 1976 figures to 1977.

"This year we all enjoying a great upsurge, even in what used to be nonmonths," said Betty Christian Hotel in Christianted and the guiding light behind Project St. Croix, a community-based effort to improve the once-disastrous tourism situation.

"For the most part, hotels in St. Croix have been booked solid from Dec. 15 through the end of March," Sperber said. "You'd got to scratch for little openings here and there, though some of the smaller places still have space."

St. Croix hotels even are enjoying advance bookings for next summer (and, in some cases, for next winter), a happy situation that also exists on St. Thomas where advance bookings have nearly all the hotels packed.

Dick Doumeng, manager of Bolongo Bay Beach and Tennis Hotel, said the occupancy at his 36-room hotel, which averages 95 per cent year round, "could not have improved, except that we have advanced bookings much further ahead. We're booked nearly 100 per cent through April 15 and have been since September."

At Lime Tree Beach Hotel, manager Mike Gaston is "looking forward to the best season ever," which will follow the best fall and the best overall year ever for the 84-room resort.

The St. Thomas-St. John Hotel Association has compiled figures that show a major jump in hotel occupancy on the two islands just from 1976 to 1977. March occupancy, for instance, went from 64.5 per cent in 1976 to 84.1 per cent in 1977, while August (usually a slow month) went from 47 per cent in 1976 to 80.1 per cent in 1977.

Cruise-ship visitors show a similar increase, with the numbers expected to leap forward again this winter season. The Virgin Islands Commerce Department says that during the last winter season close to 284,000 persons visited on cruise ships, while another 23,000 came for the day from Puerto Rico.

Those one-day visitors spent a whopping $30 million just during the 1976-77 winter season. And the 140,000 visitors who stayed at least one night spent another $50 million. That demonstrates graphically just how important tourism is to these two small islands, representing at the very least 50 per cent of the territory's economy. The third island, St. John, enjoys a relatively constant high level of tourism since its major business is the Rockresort of Caneel Bay, whose well-to-do American clientele's return year after year.

Gov. Cyril E. King, who was elected during the economic doldrums of 1974 and who died of cancer last week, believed that Virgin Islanders have come to realize the important relationship of trourism to their day-to-day lives and economic well-being, and this has played a big part in the resurgence of tourism.

"We have tried to stress to Virgin Islanders, particularly our young people, the direct correlation between government services and a lively tourist trade," King said in recent interview. "That understanding has created a marked change in attitudes here, which in turn becomes a vital factor in attracting people and bringing them back again and again because they are made to feel comfortable and welcome."

King credited other factors as well for the upturn in tourism, including more dollars being shelled out for tourism promotion, the prize-winning advertisements of Greenage and Associates, extensive programs to bring groups of travel agents and travel writers to the islands on familiarization trips and the ability of the local government to attract professionals in the tourism field.

"The severity of the winters up north has definitely woked to our advantage," said Richard Putnam, manager of St. Croix by the Sea Hotel and St. C Condominiums. Hotelier Betty Sperber agreed adding laughingly, "The minute it starts to snow in the States, our phones start ringing."

Mike Gaston of Lime Tree said the islands also have benefitted from a national economic upturn. "People in the states are spending more money and traveling more," he noted.

Nick Pourzal, manager of the 350 room Frenchman's Reef Hotel in St. Thomas, said large hotels also have been aided substantially by a change in U.S. tax laws that allows corporations to deduct as business expenses no more than two foreign conventions a year. The result has been more group business in U.S. Virgin Islands hotels, because conventions here remain tax-deductible.

Everyone benefits from that increased business - restaurants, taxi drivers, tour operators, shop owners, bars, fishing boats.

Visitors here this winter will find more pleasant shopping in landscaped and renovated shopping alleys. As for bargains, there still are many, particularly in liquors, cigarettes, crystal, china and other items; but the smart buyer will be the careful one who checks prices at home first.

Tourists also will find several new attractions this year, including Coral World, a newly opened underwater observatory that is the only of its kind in the Western Hemisphere; a well-received multimedia production called "Virgin Islands Adventure;" a very spiffy, privately owned campground at Maho Bay on St. John that is the Cadillac of campgrounds; a restored St. George Village and Botanical Gardens on St. Croix, and a just-opened St. Thomas Diving Club at Villa Olga Hotel that offers low-cost group scuba-diving packages.

But visitors may also encounter two problems that might be described as the thorns in the bougainvillea - the recurrent water shortage on St. Thomas and a recent rash of crimes on St. Croix.

Both problems are receiving priority attention from government officials in an effort to keep them well under control, but tourism interests are fearful thay they could be the territory's undoing.

On St. Thomas, the island's four water desalinization plants have been out of operation as often as they have been functioning, leaving downtown Charlotte Amalie's shops, restaurants and hotels on a system of rationed potable water - at best. During early December there was not even enough water to ration. In many cases, the hotels have been relying on their own cisterns collecting rain water and on the purchase of well water. Only one hotel, Frenchman's Reef, has its own private desalinization plant. By early January, the water situation seemed to be under control.

Though statistically there has been a drop in the crime rate this year, a recent spate of robberies has residents deeply concerned and demanding better police protection for themselves and visitors alike. So far they seem to be getting it - arrests have been made quickly in nearly every instance.

Betty Sperber is optimistic that the police are handling the problem well, but she is a realist, too.

"Tourism is a fragile industry," she mused. "We've built it up to levels that we never expected so soon. But it would only take one mistake to undo all the good we've broken our backs to accomplish in the last four years."

St. Thomas hoteliers share her concern. Nick Pourzal of Frenchman's Reef said, "Any big crime problem can wash us down the drain. It doesn't matter which island it is. We all would suffer, just as we did in 1972 with the Fountain Valley killings. People are just beginning to forget that, and they will continue to forget only if there is no recurrence."

Potential trouble spots aside - and it should be emphasized they are merely potential at this point - the Virgin Islands has one good thing going for it besides the brilliant sunshine. There has been no outbreak of the dengue fever that hit a few other islands, and the mosquito foggers are working overtime to make sure there isn't one, health officials say.