SOUTH BURLINGTON, Vt. (AP) _ Former Republican Gov. Richard Snelling announced Thursday he will run for the U.S. Senate next year against incumbent Patrick Leahy, the only Democrat Vermont has ever sent to the Senate.

Snelling called the Senate a ''cozy group where nice men and women talk about the problem and then do nothing at all.''

''If Vermonters send me to the Senate, I will speak out, shake up the system, and work day and night, to ensure that a senator from Vermont is providing the tough leadership to challenge the Congress to make the necessary decisions required,'' Snelling said at his South Burlington office.

His candidacy would pit two men polls have found to be the state's most popular politicians against each other.

''My decision may surprise some. Frankly it surprised me somewhat. One or two months ago, my answer would have been no,'' he said.

Snelling, 58, said he was motivated by a lack of action on the federal deficit, which he called dangerous ''to our country, to our children and to the realization of the American dream.''

Snelling charged that Leahy, 45, who is serving his second term, has voted for ''every spending measure.''

''Overall, I would say that Patrick Leahy has been a good senator. I have respect for him, but I don't think he has shown any willingness to make the kind of tough decisions to get the deficit under control,'' Snelling said.

Leahy was on the Senate floor Thursday and could not be reached for comment, his aides said. However, spokesman Joseph Jamele said Leahy probably would not comment, because that would only inflate the importance of Snelling's announcement.

Snelling, who stepped down in January after eight years as governor, said he was encouraged to run by Republicans who say he is the best hope for the GOP to pick up the seat next year, when a handful of seats will determine which party controls the Senate.

Snelling said President Reagan told him Wednesday '''I would rather have you run for the Senate and serve in the Senate disagreeing with me than not have you run at all.'''

No incumbent senator from Vermont has been ousted since the popular election of senators began in 1914, said Gregory Sanford, state archivist.

Leahy was elected to the Senate in 1974, and his narrow victory over then- U.S. Rep. Richard Mallary was attributed to Watergate and the resignation of President Richard Nixon. In 1980, Leahy received 49.76 percent of the vote to 48.59 percent for Stewart Ledbetter, a former banking and insurance commissioner.

Since Janaury, Snelling worked on Proposition One, a national campaign to balance the federal budget.

Snelling faces a primary challenge from Anthony Doria of South Royalton. Doria has run twice before for the U.S. Senate, both times unsuccessfully.