Mitch Snyder, the advocate for the homeless who has spent the past three years wringing millions out of the federal government, has now turned his attention to the Soviet Union. Yesterday he picked up a $5,000 check for his trouble.

During a ceremony at the ornate Soviet Embassy on 16th Street NW, Ambassador Yuri Dubinin turned over a check to Snyder from the Soviet Peace Fund, along with two brightly wrapped packages brimming with what Dubinin described as "Christmas souvenirs."

Snyder, never a shy one in the presence of government officials, surveyed the ceremonial room, with its rich woods and gilt-trimmed walls, and announced to the ambassador, "During the winter, this might make a great shelter."

"Too small, too small," the ambassador shot back, moving on to the presentation of the check.

Dubinin referred to the money as "material assistance," and said it could be used by Snyder's group, the Community for Creative Non-Violence, "for whatever charitable uses you find appropriate."

"I think I speak for everyone," the ambassador said, " . . . by expressing the hope that the day will come when there will be neither the homeless or the needy."

The issue of America's homeless came up often during the recent summit, as Soviet leader Mikhail Gorbachev denounced homelessness and poverty in this country when he was questioned about human rights in the Soviet Union.

Yesterday, Snyder was asked if he was being used as a Soviet propaganda tool in the human rights controversy. The check presentation was announced with great fanfare by the Soviets, who issued a rare invitation to the U.S. press to come to the embassy to chronicle the event.

Snyder replied that he did not look deeply into the motivations of donors.

"We don't spend a lot of time trying to determine what prompted the president to promise to renovate our shelter two days before the election," Snyder said, referring to President Reagan's decision in November 1984 to spend federal funds on the project after Snyder went on a 51-day hunger strike. "We don't spend a lot of time looking into the hearts of our Russian friends. We accept at face value the gestures that people make . . . . "

Snyder apparently has had an easier time winning the hearts of the Soviets. Snyder went on three hunger strikes before his Federal City Shelter at 425 Second St. NW was finally completed last February as the model shelter he envisioned -- with the infusion of about $6.5 million in federal funds.

This time, he said, he believed the Soviet gifts -- which included an elaborate samovar, a Russian tea urn -- were prompted by his invitation to Gorbachev to visit the shelter when he was in Washington for the summit. Although Gorbachev did not make the visit, Snyder said, he was grateful for the gift sent by the Soviet group, described as a public organization headed by a famous writer.

Snyder said the money might be used immediately for the star-studded Christmas Eve dinner CCNV has scheduled today at the Washington Convention Center, which is being lent for the occasion by Mayor Marion Barry. The group plans to serve a feast to more than 3,000 people, along with a show courtesy of several Hollywood stars, including Dennis Quaid, Cher, Valerie Harper and Whoopi Goldberg.

Yesterday, one Soviet journalist wanted to know whether the Intermediate-Range Nuclear Forces Treaty signed at the summit would have any effect on the availability of funds for the homeless.

"Yes," Snyder replied with a laugh. "I understand that for every missile destroyed there will be a new shelter opened in America."