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'."