For more than a decade, Pierre Elliott Trudeau has dominated the Canadian scene. He has served as prime minister longer than any of the other present major leaders in the western world. His craggy smile and the rose in his natty suit lapel have become almost as familiar a symbol of Canada as the maple leaf.

But now as the ripe hues of autumn here give way to duller browns and the frist snaps of chilling wind are in the air, Trudeau may be in his final months at the helm. Canada must have an election before next July and the prime minister is from all accounts - even those of some of his closest advisers - in terrible political shape.

An accumulation of troubles, ranging from the country's lagging economy, to continued uncertainties over the future of French-speaking Quebec and a simmering scandal involving illegal acts by the fabled Canadian Mounted Police, have combined to make Trudeau's Liberal Party look exceedingly vulnerable.

In by-elections last week, the Liberals got clobbered, losing 13 of 15 contests, a setback so severe that a number of Canadian pundits and politicos wondered whether Trudeau - after 10 years in office - might resign for the sake of his party even before the coming election. "Trudeau Must Go," declared the Toronto Star. Many Canadians, said a respected analyst, have developed a "visceral antipathy" to the prime minister personally - and his Liberals are paying the price.

Trudeau has survived popularity slumps before (he emerged from one to win the general election of 1974) as well as the embarrassingly public defection of his young wife, Margaret.Yet this time, say those who know him, the prime minister may not make it back. Clearly, he is feeling a strain.

ON THE FLOOR of the House of Commons Tuesday, when an opposition member quipped that the government might destroy documents in the Mounties case. Trudeau, his eyes blazing, stepped into the space in front of his desk and demanded to know who had made the crack.

"I'll kick his ass," Trudeau snapped.

(The official record of the session made the word "arse," a quainter term. But the Canadian Parliament is televised and viewers plainly heard the saltier version.)

The prime minister then smiled, the sort of nervous grin that Richard Nixon displayed after sharp exchanges with reporters during Watergate Trudeau watchers of long standing said he is usually a master of control in debate.

Problems, they concluded, "are getting under Pierre's kin."

The prime minister is not "power mad, not on some power trip," said one old friend, and if the mood of the country is as nasty come spring as it is now, then the P.M. might step aside to let someone else take the party to the polls - a sign that he has talked about the possibility in private.

The odds, though, still heavily favor Trudeau's staying on for the election fight whatever his weariness of the moment. At 59 he looks years younger than his age and is said to draw inspiration and vigor from his three sons, aged 6 and under. Giving up, those around him say, is simply not Pierre Trudeau's style.

IF TRUDEAU and the Liberals do get beaten, Canada's next prime minister will be the leader of the main opposition party, the Porgressive Conservatives. He is Joe Clark, a slender man of 39 with a receding chin who was known around the country until very recently as "Joe Who?"

"Joe is a hell of a lightweight," pronounced one of Ottawa's shrewder political observers. "Can Joe fill Pierre's shoes?" headlined an article in the Montreal Gazette, the implication evidently being that it is going to be very rough.

Indeed, the irony of Trudeau's decline is that the likely alternative apparently leaves a great many people cold also. Clark has shown undeniable skill at organizing for elections and Conservatives say he is gaining in stature and confidence as the prospect of premiership starts to loom larger.

All but the most ardent Clark supports concede, however, that he is still, as one official put it, "callow." Western diplomats and journalists here shudder at the prospect of Clark - who, the story goes, dropped out of law school twice because he would not have made it through - sitting down to bargain with the likes of Germany's Helmut Schmidt, France's Valery Giscard d'Estaing or Jimmy Carter.

"Can you image?" one political reporter remarked, "They'll eat little Joe alive!"

The consensus seems to be that the Progressive Conservatives are benefiting from what is a strong move away from a government that has simply been around too long, a widespread yearning after so many of Trudeau and company for something else. And Joe Clark is at least a change.

THE BIGGEST caveat to Clark's chances for election seems to be that the Conservatives have made virtually no dent in Quebec, where the secessionist Parti Quebecois runs the show locally and the Liberals retain the bulk of seats in the federal parliament.

English-speaking Canadians have the majority of votes across the country, but there is a sense abroad that the strains on Canada's federation symbolized by Quebec separatism would be exacerbated if the Conservatives were chosen with no backing from "Francos" as French-speakers are called.

The conventional belief is that Trudeau, French origin, could hold Canada together while Clark could not.

For the moment, however, the long-term intentions of Rene Levesque, leader of the Party Quebecois, are a little obscure. After being elected in 1976 on what amounted to an independence platform, he recently said that a referendum to be held in the next year or so would merely seek permission from people in Quebec to discuss what he calls "sovereignty/association" with the federal government. This complex arrangement is meant to greatly increase provincial powers but stops short of outright separation.

Only once those discussions were completed would Levesque put crucial issue to voters again, which means that the crunch is now years away - and Levesque himself faces a tough reelection campaign in 1980.

Levesque is under attack from radical nationalists in Quebec, who accuse him of succumbing to gradualism. Heady with the new sense of Franco preeminence after more than a century of Anglo power, the radicals feel the time has come to be decisive. It may well be, experts say, that Levesque has chosen caution.

"Holding on to power," the editor of the French-language Le Devoir wrote, "and making concessions is always superior to being idealistic and defeated."

But there is another plausible view of the wily Levesque's stategy. He and Trudeau are old rivals. By defusing the separatism issue as he has now, Levesque makes Trudeau seem less essential to maintaining Canadian unity - thereby helping to get rid of him, to bring about a Conservative government and to sharpen the French-English cleavage in the country.

All in all, as one outsider commented, its enough to make Trudeau's rose wilt.