Edward M. Kennedy's biggest victory in 1982, as his advisers see it, was not his Senate reelection in Massachusetts but his private polling in New Hampshire.

His poll in that state, where the nation's first presidential primary is held, indicated that Kennedy's new, highly unusual and costly television ads, beamed in from neighboring Massachusetts during his Senate campaign, had "significant impact" in blunting the character problems that plagued his last run for the presidency, the Kennedy camp has told prominent Democrats.

Kennedy's advisers say that could be the biggest breakthrough any of the 1984 presidential hopefuls achieved in this year's campaign. For his advisers realize that, although he leads all Democrats in the early polls, they must still convince party professionals that Kennedy can win a nationwide presidential election.

Generically, last Tuesday's election lifted Democratic presidential prospects for 1984, as Democrats captured control of big-state governorships that have proved vital to past presidential campaigns: Michigan, Ohio, Wisconsin, Minnesota, and Texas. Democrats also resurrected their 1984 presidential hopes by recapturing large numbers of voters they lost in the Reagan sweep of 1980.

Individually, the Democratic presidential prospectors used the 1982 campaign as a political grubstake for 1984 explorations. As they crisscrossed the country in behalf of the candidates of '82, they built reservoirs of good will and lists of good workers.

The other front-runner, former vice president Walter F. Mondale, who has noted that he is a prime example of unemployment caused by Ronald Reagan, traveled the country in behalf of 150 candidates this year, more than anyone else.

Sen. John Glenn (D-Ohio) launched himself to within striking distance of Kennedy and Mondale as he traveled the country signing autographs for people who were not sure where he stood but who knew where the former astronaut had soared.

Sen. Alan Cranston (Calif.), who created a group of big givers called the Democratic Leadership Circle almost two years ago, could claim that he had channeled more money to more candidates than the political action committees of Kennedy and Mondale.

Sen. Gary Hart (Colo.), who was George McGovern's 1972 presidential campaign manager, had the know-how on his travels to identify and recruit political field hands who could form a skilled corps of campaign organizers.

But the one example of 1982 salesmanship that may prove crucial to the 1984 presidential campaign is Kennedy's experiment in New Hampshire, the state that handed him his first and most devastating defeat in 1980.

The ads were designed by media expert Michael Kaye not to make people forget about the 1969 Chappaquiddick accident--in which Mary Jo Kopechne died and which will remain linked with Kennedy always, his advisers concede--but to convince them that there is another side to Kennedy.

Three different, intensely personal ads, each five minutes long, sought to portray Kennedy as a compassionate, private figure who has endured much grief. They showed Kennedy with his son, who lost a leg to cancer, and with the families of his slain brothers. "He's not a plaster saint," one ad noted.

The ads aired repeatedly on Massachusetts stations at a cost of$850,000. The Kennedy strategists were not worried about his little-known Republican opponent, Raymond Shamie, whom he defeated with 61 percent of the vote, but wanted to see how the ads played in the northern portion of that media market, which includes most of the population of New Hampshire.

Kennedy commissioned pollster Patrick Caddell, who devised the surveys and strategies that Jimmy Carter used to defeat Kennedy in New Hampshire two years ago, to see how the new ads had fared with these New Hampshire voters.

His survey showed that the ads had "significant impact" on the voters there, Kennedy advisers are telling influential Democrats. The more people see the ads, the more they believe that there is a warm, caring side to the Massachusetts senator.

The survey has given Kennedy aides their first measurable hope that they can deal effectively with the questions of character that arose in his 1980 race, and that Kennedy strategists and outside politicos are certain will arise if he runs for president again.

Kennedy's administrative assistant, Lawrence Horowitz, declined to comment on reports from other prominent Democrats about the Kennedy polling, saying the results are still being analyzed.

Within the Democratic Party, there is some question whether Kennedy's character-building commercials will work.

"Baggage is baggage," said one of the Democratic Party's senior thinkers. "Once you get it, you've got it."

But some in rival camps concede that the Kennedy poll could be significant.

"If Kennedy's polls showed he was able to improve on those personal character questions, that certainly is a big help for him," said Kathy Bushkin, Hart's press secretary.

The outcome of Caddell's survey is expected to be a major factor in Kennedy's upcoming decision on whether to run for president in 1984. Meanwhile, Kennedy's strategists are going ahead with campaign organization plans.

In the next two months, the men who have been pursuing the presidency will be arranging their official coming-out celebrations. And Kennedy will have to decide in the next month or so as well, his advisers say, because he must have a presidential exploratory committee in place by the end of January to take full advantage of federal matching funds for a presidential campaign.

Meanwhile, questions about which 1984 presidential candidate did himself the most good in the 1982 campaign produced uncharacteristic magnanimity in a Democratic Party that is frequently more fractious than fraternal.

"If anybody got a bit of a nudge out of 1982 it has to be Mondale -- he did more," said political consultant Robert Keefe, who has recently joined Glenn's presidential cause.

At the party's midterm convention in Philadelphia last June, Keefe was at the forefront of those who advertised their uncommittedness by wearing buttons that said: "Wait in the Weeds, Gang." But now Keefe explains: "I'm out of the weeds. I'm helping Glenn. But I have to say that I guess Mondale was in more places, saw more people, and did more things than any of the rest."

The Mondale camp shares that view. "Mondale had a terrific '82 campaign," said his chief adviser, James Johnson. "But the most important result of the 1982 elections is that it concluded the rebuilding of the confidence and morale of the Democratic Party."

For Glenn, 1982 may be remembered as a year of missed opportunities. He was slow to organize and slow to develop the savvy sort of staff necessary for a serious run for the presidency. He has not lost ground, but he has lost time.

Keefe recognizes this view, which is widely held by his fellow pols. But he promises: "Glenn has finally made that internal commitment to go all out. Glenn is in the process now of figuring it all out . . . putting his campaign together. Coming out of Philadelphia the midterm convention , his money guys beat up on him. Now he's going to do it right."

Presidential politicking is imprecise, and so old hands put stock in such time-tested values as the ability of governors to elect presidents.

"Regardless of who gets the Democratic nomination," said Democratic insider Robert S. Strauss, "the governorships we won in 1982 could be the biggest thing we have going for us in 1984."