After suffering their worst winter in recent memory, Washington's hotel operators are beginning to see an upturn in the city's vital tourist trade.

With only 14 percent of Washington's tourism business tied to traditional sightseers, the city's hotel business has been especially hard hit by a reduced number of business travelers and convention goers.

"The first three months have been off considerably," says Leonard Hickman, executive vice president of the Hotel Association of Washington, D.C., which represents 58 hotels within the District's boundaries. Hotel occupancy in January was down 16 percent from last January, he said, down 12.7 percent in February from a year ago, and down 13.5 percent in March. "It's the lowest since we began keeping occupancy statistics in 1946."

Area tourism officials blame the sharp drop in business this winter on terrible weather nationwide, on the recessionary economy and on federal budget cuts--key factors in reducing business travel. Business travelers and convention goers make up 86 percent of the tourist business in the Washington area, according to a study done for the District government last year.

Although the decline in the number of visitors here this winter was significant, some say that certain factors came together to exaggerate the size of the decline, and that the poor showing may not signal a continuing slump for the Washington metropolitan area's tourism business in 1982.

Take January's 16 percent decline in hotel occupancy, for instance. Because of President Reagan's inaugural and the festivities that accompanied it, hotel occupancy had jumped 7 percent in January 1981, according to Laventhol & Horwath, which puts out a monthly Lodging Industry report for the metropolitan area. So this year's decline was off an unusually enlarged base.

Also, Congress returned to Washington Jan. 25, almost three weeks later than the Jan. 5 start-up of its 1981 session, undoubtedly affecting a substantial amount of travel to Washington during the month.

On top of the bad winter weather, the Jan. 13 crash of an Air Florida jet into the 14th Street bridge during a snowstorm and frequent icy-runway incidents at other airports didn't help, and appear to have discouraged travel and caused cancellation of some already booked travel plans, airline and hotel officials say.

Too, the number of hotel rooms in the metropolitan area has been increasing so that more hotel rooms are available and being counted each month in the overall pool. "If you're increasing the supply without a corresponding increase in demand, occupancy is going to go down," says William Harrington, of Laventhol & Horwath. L & H's report on January occupancy showed a 20 percent decline in the District and an 18 percent decline for the area.

Altogether, there are now about 15,500 hotel rooms in the District, up about 1,000 from last year, Hickman said. New hotels include the 350-room Washington Marriott, the 164-room Georgetown Marbury House, and the 360-room Ramada Renaissance. There were also hotels opening in the suburbs, boosting the number of rooms in the area to about 38,000. New entrants include the 740-room Crystal City Hyatt Regency and two large Marriotts, one at Tysons Corner and another in Gaithersburg, that may have drawn some business away from the District. They aren't included in the Washington Hotel Association's purview.

"It all means there was a decline, but not 16 percent," says Austin G. Kenny, executive vice president of the Washington Convention and Visitors Association. "However, unquestionably there was some overall decline in the number of visitors to Washington . . . a sharp decline."

Now, however, there are signs of a pickup, starting with the airlines, whose officials--with their fingers crossed--are reporting increases in passenger traffic.

If it keeps up, it will be good news for the hotels, since more than half of their guests come to Washington by air, according to last year's survey. An even larger portion, about 79 percent, of the business-related travelers come by air. "Those persons who don't sit in those seats don't lie in our beds," noted Edward F. MacMillan, partner and managing director of the 340-room International Inn.

Officials at area airports also detect an upswing. Formal numbers aren't available yet for recent traffic at Washington National and Dulles International airports, according to James A. Wilding, director of the Metropolitan Washington Airports for the Federal Aviation Administration. But everybody exposed to the traffic at the two airports has felt a general improvement in the last 30 to 45 days, he says.

"There are pieces of information: the parking lots are fuller, there are more people around, the skycaps are whistling . . . you sense the whole tempo is picking up. We're on some sort of upswing--more than just coming out of the winter doldrums," he says.

That's reflected elsewhere in Washington, too:

* Attendance this month at the three most popular of the Smithsonian Institution's facilities--the Air and Space Museum and the museums of American History and Natural History--is running ahead of last April, based on figures for the first 11 days of the month. "The winter doldrums are over as far as we're concerned," says Gilmer Van Poole, building coordinator for the information desks at Air and Space and the Hirshhorn museums. "It's as busy as it's been any year in the recent past."

* Tours of the White House are "just packed," according to Carol McCain, director of the White House Visitors Office. Daily, the White House can take 200 on group tours and 1,200 ticketed through congressional offices. "We are constantly booked; we don't have another ticket to give out," McCain said. "This is my second year here, and this springtime is every bit as frantic as the first, if not more so."

* Ridership on the tourmobiles has returned, making Tourmobile President Tom Mack think that he's going to have a "good year" after all, even if it doesn't match last year's "phenomenal" performance. A combination of the poor economy and the bad weather made the winter awful. The operation was forced to close down 13 days, compared with a normal shutdown of three days a year. "One doesn't usually make up that much ground," Mack said. "Still, our April performance indicates we are going to do pretty well." After a 60 percent decline in ridership in January and a 35 percent decline in February, there has been a "dramatic" change and ridership so far in April is running ahead of last year's. Total ridership from Jan. 1 through April 17 still was down 7 percent.

The increased activity also has been reflected at area hotels: many are totally full. One travel agent reported having difficulty booking a single room at a good hotel in downtown Washington last week. Airline representatives working on June airport schedules met last week for two days at the Gramercy Inn after calls to 41 other hotels failed to turn up a meeting room to hold 100 persons. Meeting participants had to scatter to many hotels for rooms. "We couldn't even get in at the Dulles Marriott, would you believe?" one official said.

Contrary to many hotels' winter experience, occupancy this year at the Marriott Corp.'s hotels, nationwide and locally, discounting the snowy January, is running ahead of 1981, knowledgeable sources say.

"We're not doing too badly," says Penny Cummings of the 1,505-room Sheraton Washington Hotel, the District's largest. The demand for group business, the hotel's mainstay, is stable, she said, although the hotel has seen a drop in attendance at meetings and an increase in the number of people who cancel their reservations or don't show up. Although summer is not their best period, "we're doing very well this summer," she said. "It looks pretty good for the rest of the year." Business this winter was off more at the hotels that cater to a more transient business, such as the Sheraton Carlton, she said.

The International Inn's McMillan said business dropped considerably last fall and remained down until the second week in April, adding that the independent hotels may have suffered more than the chains. "Now we're doing very well," he said. The hotel has been having some 100 percent-full nights and was sold out all last week, he said. Both convention and family business have picked up.

Philip A. Wagner, general manager of the Gramercy Inn and the Executive House, also says business has been off since last fall and that it's now picking up. His hotels, which don't have convention facilities, cater to tour groups and families and government and business travelers. His hotels are down about 11 percent to date--mainly in the government and business travel areas--but busier now. "We're a little ahead of the season now, but I'm optimistic," he said. "Bookings are heavy . . . although cancellations are higher this year."

Business for the 800-room Shoreham, now in the midst of a $15 million renovation by the Dunfey chain, is also picking up, according to Managing Director Charles J. Barren. It's busy enough that he's putting off renovation of other rooms until next winter. Business was "slack" in the first part of the year, with a cutback in government and corporate business, but it's returning, he said. "We're looking at a very good spring, a good summer, and a very good fall."

Although it's too soon to tell, many officials of hotels and tourist-related activities believe the poor winter has resulted in a pent-up desire for travel, and that Washington, with its abundance of free activities and easy access, will benefit. Some suggest that a continuing poor economy might even boost the area's tourism from the heavily populated East Coast, if families and other vacationers scale down plans to go West, to Europe and other farther destinations.

Some of the business the hotels have relied on in the past, however, may be lost for some time, possibly permanently--a consequence of the reduced budgets for federal travel and meetings and the plan to shift some federal programs back to the states, says Emily Durso, an official of the District government's Office of Business and Economic Development. "The market's changed; the hotels know that they can't count on the business and government travelers." But she's optimistic about the future. There will always be a "guaranteed market" here for U.S. and foreign visitors because of the city's attractions as the nation's capital, she says. Hotels that cater to a large family trade are doing well, she notes. "That's the traffic the city's going after."

Washington currently is gearing up for a significantly more aggressive campaign to attract convention and tourist business. Aided by a $298,000 grant from the District government, the Washington Convention and Visitors Association, a trade association, is conducting promotional activities for the new Convention Center, which is to open late this year.

The District's promotional efforts, however, pale when compared with the promotion budgets of other major cities, some of which approach $3 million a year, not counting the help cities may get from their state tourism agencies. The Smithsonian, the National Park Service and other agencies here, however, take up some of the slack.

That will soon change if the City Council adopts a proposal by Mayor Marion Barry and recommended by the hotel industry to increase the hotel occupancy tax from 80 cents to $1. "I don't think there will be a problem with it because it's a tax on people from out of town," one District source said. The 80 cents collected now goes into a fund that has been used for land acquisition for the Convention Center.

The new proposal earmarks 60 cents of each dollar to the operation of the Convention Center and 40 cents to tourism promotional activities. The Washington Convention and Visitors group would get about $930,000 a year for its activities, almost three times what it now receives from the District. The Mayor's Committee to Promote Washington would get approximately $700,000 for promotional activities.

The committee, now operating with a $100,000 grant, will kick off a "Washington is a Capital City" campaign on May 3. "At a time when there are fewer federal jobs and decreased federal spending, it makes sense for us to turn to our second largest industry--tourism--and take advantage of its enormous potential," says R. Robert Linowes, the committee's chairman.

A lot of hope is riding on the $98 million Convention Center, which can hold up to 20,000 people, and the accompanying hotel development. Already, 50 conventions are booked in the center over the next six years, including some very big ones. In 1985, for example, the center will host a seven-day American Heart Association conference with some 15,000 people expected to attend, using 7,500 hotel rooms.

There is good reason for Washington, with its lack of industrial base, to promote tourism and hotel development. More than 17 million tourists and business travelers are estimated to have come to Washington in 1980, generating more than $2.4 billion in business revenues and $43 million in for the District government.

The tourist industry directly supports almost 32,000 jobs, and promises to employ many more with the opening of the Convention Center.

Hotels also are always spending money on upkeep and furnishings. "That's another reason we like hotels," Durso said. "They have to spend and spend and spend."