MANCHESTER, N.H.--Sen. Gary W. Hart (D-Colo.) yesterday shocked heavily favored Walter F. Mondale, decisively defeating the Democratic front-runner in New Hampshire's first in the nation presidential primary.

With 96 percent of the precincts reporting last night, Hart held a 41 to 28 percent lead over the former vice president, with Sen. John H. Glenn (D-Ohio) a distant third at 12 percent.

President Reagan, benefiting from a from a major write in effort by Granite State Republicans, won a surprising 5 percent of the Democratic vote in this heavily conservative state.

About 100,000 voters went to the polls yesterday, as turn-out was lowered due to heavy afternoon snows.

Behind these three leaders came

*The Rev. Jesse L. Jackson at 6 percent.

*George S. McGovern at 6 percent.

*Sen. Ernest F. Hollings (D-S.C.) at 4 percent.

*Sen. Alan M. Cranston (D-Calif.) at 3 percent.

*Former Florida Gov. Reubin O Askew at 1 percent.

Hart's impressive victory is a major setback for Mondale, who was so confident of victory here that he spent most of the last three days out of the state Mondale had been considered one of the strongest Democratic front runners in recent decades, and many analysts had expected him to lock up the nomination long before the party's San Francisco convention this summer.

No candidate in more than 30 years has won the Presidency without first winning here.

Hart, who conducted a strong grass-roots campaign in New Hampshire over the last 18 months and stressed new ideas and leadership, appeared before cheering chanting supporters in Manchester's Chateau Lounge.

"New Hampshire voters are cantankerous they're independent they make up their own minds. They're also smart," Hart told the youngish crowd.

But Hart added, "I'm not prepared at this moment to take the label of front runner Hart said, however, that he had buried the label of 'dark horse'."

In a victory speech filled with references to John F. Kennedy '40 and Franklin Delano Roosevelt '04 Hart said New Hampshire voters, had the power to change the course of American history.

Not Quitting

Mondale, who found out that be had lost while attending a fundraiser dinner in Boston flew to Manchester early yesterday evening. At a pre flight news conference at Logan Airport a somber Mondale vowed, "I'm going to be campaigning all out because I believe I will be nominated.

The reason I'm confident is that what I'm saying and what the American people want is the same," Mondale added.

Glenn appeared downcast at an evening press conference at the Sheraton Tara telling reporters he was hurt by the Reagan write in votes.

I hope all these people come home to roost in November." Glenn said Glenn and his staffers took whatever solace they could find in the Mondale defeat, saying that the idea that Mondale had the nomination "all locked up" had been proved wrong.

Calling the primary the beginning father than the end. Glenn echoed one of Hart's criticisms of Mondale, saying, the politics of the past were proven to be exactly that the politics of the past."

"I am not considering dropping out," Glenn said, surrounded by his campaign brass. "I'm going to the convention in San Francisco and I'm going to be the nominee."

Glenn staffers last night said the senator will concentrate on winning delegates in southern states, especially Alabama, where the former astronaut has a strong organization.

New Hampshire Campaign Director Paul Shone said Glenn is still a factor in the race for the Democratic nomination because of his national reputation.

Hart's triumph must be ranked among the most stunning upsets in primary history. McGovern was considered in have won a victory in the New Hampshire Democratic primary in 1972, even though he lost by six percentage points to the then front runner, Sen. Edmund S. Muskie of Maine.

McGovern capitalized on the second-place finish to run up primary and caucus victories around the country and eventually capture the party's nomination.

Hart, who managed McGovern's campaign that year, will now be thrust into the media spotlight and may be able to bolster an organization that is weak in many important primary states, analysts speculated last night.

Unlike McGovern, however, Hart will be encumbered by new campaign rules which make it difficult for candidates to raise money quickly. Moreover, Hart does not have full delegate slates in a number of states.

Gary R. Orren, associate professor of public policy at the Kennedy School, said that despite a victory that dwarfed McGovern's 1972 showing. "It will be very difficult--but not impossible--for Hart to win the nomination."

The next major test for Hart is so-called Super Tuesday on March 13, when 10 states--including Massachusetts and Florida--hold primaries or caucuses. Mondale and Glenn hold full delegate slates in all those states, while Hart has only partial slates in Florida and in later important states Illinios, Pennsylvania and New York.

Before Super Tuesday, Maine and Wisconsin will hold caucuses and Vermont holds a primary preference poll Tuesday.

Susan Casey, deputy state co-ordinator for Hart, said at Hart headquarters. "As far as the delegate slates are concerned, it doesn't matter It's no problem."

Charles B. Finch. Hart's New York field co-ordinator, promised that the Coloradan will be able to compete for 90 percent of the delegates" in the Super Tuesday states.

But he added that Illinois where an important primary will be held March 20, "might be a problem."

They're always a little cantankerous," he said.

Hart, whose politics are considered slightly more conservative than Mondale's traditional liberalism, has not been seriously scrutinized by the media and the other candidates.

No Lumps

Orren said Hart has "not received his lumps yet," adding that the Coloradan's late support for a nuclear freeze may be brought up by critics.

Steven D. Stark a lecturer at the K-School and a former campaign issues adviser to Jimmy Carter, said Hart, like Carter, will have to handle correctly his new found recognition.

"As with any new fact that curries on the scene very quickly, there's the problem of not turning out the way they wanted him in," Stark said.

Stark added that Hurt is succesful because "he us not running a traditional liberal-conservative race."

"He has transcended ideological boundaries," Stark said.

George Brune, New Hampshire's State Democratic Party chairman, said at Mondale headquarters in Manchester that Hart profited from the "one-on-one" nature of New Hampshire campaigning.

"Hart beat Mondale because Hart poured himself into New Hampshire," Bruno said. "After New Hampshire, the race is a media event."

Robert Beckel, Mondale's national campaign manager, credited Hart with "having the perfect ways," adding that Hart profited from weakness in the rest of the field.

"We believe our potential here was between 30 and 40 percent," Beckel said, "and we didn't expect Glenn would do as badly as he did in Iowa."

Beckel predicted. "Hart won't do well in the South or in the industrial states."

In the delegate competition, Hart won 10 delegates and Mondale eight. None of the other contenders reached the threshhold needed to win delegates. Mondale still holds the overall lead for the nomination, with an estimated 180 to 36 for Glenn and 25 for Hart. There will be about 4000 delegates at the Democratic National Convention in San Francisco this summer.

The Stragglers

For the rest of the eight-man Democratic field, yesterday's results may mean the end of the road Cranston announced an "important" news conference for 7:30 a.m. this morning, and there is speculation that he may drop out of the race.

Cranston who had put much of his resources into Iowa was dealt a major setback with his fourth place finish Cranston, who had hoped to use a strong Iowa showing to slingshot his candidacy beyond dark horse status was even weaker in New Hampshire.

Jackson and McGovern, who battled for fourth place as results trickled in throughout the evening will probably stick it out until Super Tuesday.

McGovern won only Massachusetts in the 1972 general election, and he is considered strong in this state this year.

"I have said since 1972 that the wisest voters are in Massachusetts," McGovern joked before supporters.

Hollings and Askew told supporters their campaigns will continue.

In addition to winning several thousand write in votes in the Democratic contest. Reagan won against three minor opponents in the Republican primary.

Paul Duke Jr., Peter J. Howe, and John N. Rosenthal contributed to this report