Solar energy advocates, delighted by the most vicious winter in 37 years, say they are now convinced their industry is on the edge of a major breakthrough in public acceptance and commercial use.

Official government reports are partially confirming what solar energy pioneers have contended for years - that solar heating can be economically competitive - and operating solar projects are proving to be dependable under the strain of a harsh winter.

Major corporations have begun million-dollar advertising campaigns for solar equipment, lending the weight of well known names to the efforts of existing small companies to over-come the traditional resistance to change in the American public.

Utility bills for all-electric homes - about half of new home construction - have skyrocketed, oil prices have climbed and natural gas prices promise to follow, leaving homeowners worried about conventional systems and curious about alternatives.

"We've had mild winters and no problems since the 1973 OPEC oil price shock until this year," said Ronald Scott, assistant director of solar heating and cooling at the Energy Research and Development Administration (ERDA). "Now everybody is hurting.

"A lot of people are afraid because this is a new industry and a lot of people are waiting to see what Congress is going to do about tax incentives," Scott said. "The combination makes everything sit on the ragged edge."

A tax incentive could trigger a boom, Scott and others said.

At Gruman Sunstream, the solarwind division of the aerospace giant, public affairs director Joseph Dawson predicts a tripling of the solar energy market this year.

"The whole industry really started in 1973 and we had our first convention in 1974," Dawson said. "There were Rube Goldberg contraptions all over the place. By last year the equipment was sophisticated and well designed. It was like jumping the auto industry from 1900 to 1930 in two years."

Most of the present emphasis is on solar heating for hot water, a simpler business than heating an entire home, ERDA's Scott said.

"Basically we're finding that even in the extremely cold weather the systems are performing well."

One system is in its second winter of operation at the Madeira School near Great Falls, Va. There, a slanting roof covered with solar collectors heats oil, which heats a hot water tank. On a recent warm, sunny day, the solar system was keeping a 10,000 gallon tank at 100 degrees. The system is supplemented by an oil-fired boiler in a nearby gymnasium so it is difficult for school officials to judge exactly how much is saved on fuel bills, a common problem in attempting to determine the economic feasibility of solar energy. ERDA is now monitoring several buildings to try to gain precise data.

Madeira's business manager, retired Adm. William O. Snead, estimated that the extra cost of solar heat equipment would be paid back in fuel savings in about 20 years.

The science building, highly praised architecturally and built entirely with private funds, "over the long term will pay us back, and at the same time the building itself is a teacher of science," said Cecile Banner, director of development at the private girls' school.

The combination of trying to save money while doing good ecologically, is common in the solar heat world. At the Maine Audubon Society's new headquarters in Falmouth, heat is provided by solar panels and a wood-burning furnace.

So far, this year the building has required fewer than four cords of wood at $70 a cord, said Erika Morgan, the energy information coordinator.

"We have had some bugs - small air leaks, but we've solved that now. We wanted a design simple enough for Joe Sixpack to do on his own house, and we wanted our building to be a statement in support of renewable energy resources," she said.

A local pioneer, Juergen Haber of Washington has had a more troublesome leak. His system was designed and built by a group of friends and experts that failed to include a plumber.The pipe used to bring solar-heated water down from the roof was designed for cold water, not hot, and leaks developed just as the coldest of this winter's weather hit.

It is the sort of incident that frightens people who are about to put $60,000 or $100,000 into a new home and want to know that everything works.

There are other problems that could be associated with solar heat. One would be the appearance of solar heat collector panels on rooftops. Advocates contend panels would not be as unsightly as television antennas. Another problem would be possible legal fights over sunlight. A property owner "owns" the air space over his own land, but sunlight arrives at an angle.

A recent ERDA report, containing complex calculations on comparative costs, found present technology for solar heating more economical than electric heating in Washington and most of the United States Oil and gas were cheaper.

Two of the major assumptions the report were that fuel prices would rise 10 per cent a year and that solar heating now costs about $20 per-square-foot of collector area.

If solar coast could be cut to $10 per-square-foot of collector area, solar heat with all present heating methods in most of the nation, according to the study.

While some critics argue that the ERDA report is too optimistic about solar energy, Harry Thomason, perhaps solar energy's most outspoke crusader, contends that the figures in the study are out of date.

Thomason, who bitterly accuses the government and the major oil companies of holding back solar development, has built six solar houses in the Washington area and says that about 200 using his designs have been built across the nation. His houses include air conditioning, and the only supplemental form of heat is a gas or oil hot-water heater.

Thomason, who built his first fully solar home in 1959, contends that he can build a house with his special designs and patented ideas for less than the cost of a conventional home. A home he built in 1963 used $10 worth of oil and stayed warm in January.