The long and futile quest that began in the snows of Iowa ended today with the coldness of a Minnesota storm. Walter Mondale had spent 22 months pursuing the presidency, but tonight even his home territory remained in doubt as he was crushed by Ronald Reagan in state after state.

In his graceful, sad concession speech he praised the America that voted for Reagan -- and shushed the boos that followed mention of the president. The sad, mostly dry-eyed crowd of about 2,000 was dwarfed in the cavernous St. Paul Civic Center, pushed to the front as if to create mass for the TV cameras.

Praising Geraldine Ferraro, Mondale said, "We didn't win but we made history and that fight has just begun." And, later, "I'm at peace with the knowledge that I gave it everything I've got."

* And he spoke to his youngest supporters: "I know how you feel because I've been there myself. Do not despair. This fight did not end tonight, it began tonight. I have found that in the seeds of every victory are to be found the seeds of defeat, and in every defeat are to be found the seeds of victory. Let us fight on."

Hundreds of supporters who had flown here to be with Mondale on Election Day, at the end of his quest, joined him earlier for a dinner in the ballroom of the Radisson Plaza. A light display spelled out "To sir, with love," but the magnitude of the defeat spelled out the saddest message of all. Some wept, according to those in the room, when Mondale said, "I know that you did this because you believe in a better America. You've learned more in the last year and a half than you could have in a lifetime."

As Mondale returned to the Radisson Hotel, his face ruddy, his smile pasted on, he was followed closely by campaign manager Robert Beckel and chief speechwriter Martin Kaplan. Their arms were flung around one another in camaraderie. Joan Mondale and the Mondale children had arrived earlier for the dinner, the press shouting questions; Joan Mondale put her hand over William Mondale's mouth.

The deep sadness and depression here were not just for Mondale's loss but for what the coast-to-coast sweep could portend for those who clung to the traditional values of the Democratic Party. The size of the mandate and all that it seemed to represent were frightening to many here -- to the kind of the people who cheered Mondale's message across the country. And they cheered tonight when he conceded, saying, "Tonight especially I think of the poor, the unemployed, the elderly, the handicapped, the helpless and the sad -- and they need us more than ever tonight." Yesterday, he said, "If you let them make history, they'll turn your vote into a future you never wanted." Tonight, he added, "Let us continue to seek an America that is just and fair." At the Arena

Knowing it was over, a sparse crowd gathered at the Civic Center hours before Mondale was scheduled to speak, as if to pick up relics of a failed campaign. They seemed stunned by what was happening. Pat Marcus, a housewife, said that some of her friends voted for Reagan. "A lot was personality and I can't understand why. I asked them! 'Well, he's done okay. We're not at war.' " She was sitting on the floor playing pinochle with her husband and another couple.

The arena was draped in Mondale-Ferraro banners. One huge sign said, "Teach your children well," and handmade placards displayed campaign slogans. A brisk business was going on at the button booth for what would be collectors' items. Sandra Bates, a young secretary buying a "Jane Wyman Was Right" button, shook her head, saying, "People have really gotten duped by TV. They are not paying attention to what's happening in this country." What bothered her most? "Oh dear, how can I pick one thing? Reagan hasn't done anything for the common man and yet the common man is who seems to be suporting him." Before the Voting

This morning, Mondale had breakfast with campaign aides, his family and old Minnesota friends -- a Mondale Election-Day tradition for 20 years. In late afternoon, in the lobby of the St. Paul Hotel, senior adviser John Reilly appeared in good spirits before running into Mondale campaign chairman James Johnson. The two conferred in a corner while members of the press tried to listen; Johnson, with a weak smile, told reporters, "You could get two to five in this state for loitering."

Johnson left to bring Mondale to the dinner. Reilly headed for the elevator, looking dejected. Finding the Formula

Yesterday, Mondale begged his last audiences not to give Reagan a mandate, hoping to stave off the rout that threatened to send him into history as the nation's biggest loser -- falling even below George McGovern, who won only one state and the District of Columbia in 1972. Beyond that, he was battling for what he believed in.

In the end, it mattered not. Those massive crowds that showed up from Boston to Seattle proved to be the heart of his constituency rather than the crest of a quiet groundswell waiting to vote. Mondale may not have been the best candidate, but any challenger would have faced two formidable obstacles: the public's perception of present and future prosperity and Reagan's immense popularity, which has confounded his critics and political opponents throughout his public life. In the next four years, Democrats will scramble to find the right candidate -- and the formula that could combine the party's appeal to compassion with programs that voters will buy. And although Republicans of the right will claim victory today, they must look to a future without Reagan. It is hard, at this moment, to imagine a successor from the ranks who could match his appeal. In the Beginning

It wasn't meant to end this way. Last winter, Mondale's machine -- one of the most organized, endorsed and best-financed campaigns in history -- rolled out of Iowa in first place. There were signs all along that his support was weak, but Mondale insisted that he had a mandate as he headed into New Hampshire. There, instead, he found Gary Hart, though he acted as if he had moved beyond primaries and into the election: "I am ready for Reagan," he said. New Hampshire voters prize the power of their first-in-the-nation status. Like George Bush four years ago, Mondale made the major mistake of leaving New Hampshire before the main event.

From then on, it was a battle straight to San Francisco. Yesterday, Hart urged a Los Angeles rally to cast a vote for "decency" and "my friend" Mondale, but the divisiveness of the battle had taken its toll and given the Republicans much ammunition.

The glow that came with the selection of Ferraro was marred by the fiasco of picking Bert Lance to chair the party and by the disclosure of John Zaccaro's financial problems. Mondale's gamble -- telling the world that he would raise taxes and so would Reagan, although Reagan demurred -- proved to be superb grist for the Republicans. The campaign did not start rolling on his campaign until after Labor Day and didn't hit his stride until he jolted Reagan in the Oct. 7 debate. "Louisville Slugger" was painted on his airplane and Mondale took a fighting message to the nation.

It was too late. The battle cry became, "Polls don't vote, people vote," but when they did, it was a triumph for Reagan. Now there will be the clean-up details, and the press will ask what went wrong and what the future holds. The cameramen will pull the plug, the lights will dim, the last stories will be written, the notebooks put away.

For Mondale, the dream is over.