On virtually any cool day in midtown Manhattan, furs shimmer on the bustling streets in such numbers that it's startling even to a jaded Washingtonian. During winter, flashy full length furs seem almost as much a part of this city's attire as the small headphones that block the clatter of New York traffic from the ears of thousands.

In fact, the nation's fur industry, with most of its 600 manufacturers centered in a dozen-square-block area of central Manhattan, had its first billion dollar year in 1981, and this year industry leaders seem almost oblivious to the slumping economy.

Based on the tone of the largest American fur show, which opened here over the weekend for an expected 25,000 visitors, there seems little doubt that despite--perhaps in part because of--difficult economic conditions, the business will again set new records this year.

This is a depression-proof business at this point," said Kenneth Wagner, president of Wagner Fur International and founder of the four-year-old trade show.

"We're catering to monied people, even though the lower echelon of furs may not be doing all that well in depressed areas," Wagner said. "There is a need to relieve peoples' fears. Furs do that."

But industry experts attending the opening of the American International Fur Fair noted that this year's fur fashion designers are emphasizing shorter jackets and three-quarter length coats, an effort, in part, they say, to maintain the growth of the fur business despite the nation's beleaguered economy. "There's a softness in the middle," complained one buyer, who emphasized that top of the line furs continue to sell well.

On the other hand, coats and jackets with large padded shoulders and grand collars simultaneously dominate the finest furs, demonstrating the fact that many manufacturers are doing anything but cutting corners.

"People buy high priced jewelry all the time and for high priced furs people have money," said Gary S. Kugler, executive vice president of the American Fur Industry.

There were few indications at the flashy show that the fur industry is worried by high unemployment and the overall economic slowdown, though high interest rates concern furriers as much as other business officials.

Mike Michaelson Associates Inc., a fur buying firm in Manhattan, said in an open letter to fur retailers published in "Fur Age Weekly" that sales continue to rise in the industry for a variety of reasons. Michaelson cited "an economy which almost forces people to spend money on luxuries; a greater sense of independence among women, many more of whom are buying their own furs, and the rise of the more-than-one-fur wardrobe" as among the reasons for the industry's recent success.

Furriers also tout their business as one with a favorable balance of trade, with 1981 American fur exports totaling $487 million, a little more than double the nation's fur imports. The industry, in fact, is urging U.S. trade officials to ask Japanese officials to lower or remove a 20 percent tariff now assessed on furs and garments entering Japan, pointing out that Japan produces virtually no furs.

No major trade fair here would be complete without either a Japanese contingent or some degree of political controversy, and the fur show's opening brought out chanting picketers demonstrating against the industry's treatment of animals. "Make your fur fake for the animals' sake," about 50 protestors shouted at one point, winning the attention war by getting their minute on the local news the other night.