Nancy Reagan toured a display of art donated by fashion designers at the National Museum of American History last night. But the photograph she acquired at this benefit auction was not on view for others to see and she shared it with no one.

Tony Weinberg, who was a writer in summer stock where Nancy Reagan was an apprentice in the early 1940s, approached the first lady as she stopped in front of a group of fashion sketches. "If I showed you two pictures of Nancy Davis, would you sign one for me?" Weinberg asked the surprised first lady. She nodded skeptically, and he produced two snapshots taken many years ago when they were both in summer theater in Gloucester, Mass., on Cape Ann.

"Would you like them?" Weinberg, now a greeting card sales representative, offered graciously. "I couldn't take them from you," Mrs. Reagan replied, and they agreed to each keep one. Mrs. Reagan folded hers, which showed her in costume, and slipped it into her silver minaudiere. Weinberg put his, a photo of her in a jacket and skirt, back in his tuxedo pocket jacket.

This was the only freebie at last night's auction, called Vernissage IV, held to benefit the First Ladies Fellowship, a program initiated by Mrs. Reagan at the time she donated her James Galanos' inaugural gown to the Smithsonian's First Ladies exhibit.

Mrs. Reagan didn't recall the plays on the schedule that summer she and Weinberg were in the theater together, or even the year the pictures were taken. "I certainly remember the dining room at the hotel," she said. "The actors had to sit off to one side and were offered food different from the rest of the guests."

She asked Weinberg how long ago the pictures might have been taken, and when he suggested 40 years back she quipped, "I was a mere child, barely out of knee pants. Wait 'til I show these to my husband."

Mrs. Reagan was wearing a black satin blouson and long skirt, also by Galanos, as she toured the art assembled by Washington Fashion Group with Jonathan Prude. Prude, a professor at Emory University, is the first recipient of this new fellowship.

Nancy Reagan admired the sketches of Auguste Leiber, husband of handbag designer Judith Leiber. "I can't even draw stick figures," she said to Prude. "My husband's really good at it."

At a Bill Blass drawing of a basket of flowers she commented, "I had no idea he did that."

The more than 400 guests, many of them Washington's fashion faithfuls, bid generously on the art. Some chose the same designers whose clothes hang in their closets, others simply liked the work on its own merit. Boutique owner Dolly Kay put a $500 bid on a Zandra Rhodes poster, "because she's a good friend." But it wasn't enough. She didn't get it. Helga Orfila bid on a poster by Razzia. "I think it looks like me," she said proudly. Just the same, her bid was also too little.

Smart money was placed on a fabric collage by Koos Van Den Akker, a fashion drawing by Willi Smith, and from Bonnie Cashin, "Self-Portrait in a Dark Moment."

Hecht's vice president Nancy Chistolini, regional director of the Washington Fashion Group that organized the auction, said she expected the evening would raise at least $10,000 for the fellowship. "It is the effective conversion of a social event into a scholarly opportunity for a first-class scholar," said Roger G. Kennedy, director of the Museum of American History.