Voters in the wheat-growing province of Manitoba on the cold Canadian prairies go to the polls today to decide whether to oust or retain the socialist government.

The provincial election pits an admirer of President Reagan against the incumbent premier, who is a member of a Canadian political party with formal ties to European socialist movements.

Both have attempted to blur their differences and both attack one another from left and right. But the campaign has provided a good illustration of how the existence of an institutionalized left in the form of the New Democratic Party is a feature of Canadian politics that makes it strikingly different from the political system in the United States.

When asked, Manitoba Premier Howard Pawley -- whose position is comparable to governor in the United States -- will describe himself resolutely as a democratic socialist. But as he campaigns for a second term, Pawley tends to talk more about the rapid growth in private capital investment since he led his party to power in 1981.

His campaign aides also proudly circulate recent strongly optimistic forecasts for the provincial economy made by analysts at Canada's two biggest banks.

His principal opponent, Gary Filmon, leader of the provincial Progressive Conservative Party, criticizes Pawley for running up a budget deficit of about $400 million and for imposing a 1.5 percent payroll tax on businesses.

At the same time, however, Filmon also accuses the socialist government of "neglecting" and "starving" Manitoba's elaborate health and social welfare system. He has promised to expand day care programs and services for the elderly, buy more expensive medical equipment for provincial hospitals and restore subsidies to chiropractors that were cut back by the socialists.

Filmon said he had decided against running a campaign strongly opposing socialism. That was the aggressive -- and losing -- strategy tried by the Conservative Party's last premier of Manitoba when he was defeated in 1981 in his bid for a second term.

"Here people seem to tune out to that message," Filmon said. "We're in a democratic country. The talk of socialism doesn't seem to have a sting."

Socialists not only control this province but they are also a significant force in Saskatchewan and British Columbia, where they have formed governments in the past. In Ontario, they joined forces with the Liberal Party to oust the Conservative Party, which had been in power there for 42 years.

Support for the socialists has been negligible in Quebec and marginal in most of the Atlantic Coast provinces. They never have risen above third-party status in the House of Commons in Ottawa, but they often have played a very influential role in national politics -- far out of proportion to their numbers.

National New Democratic Party leader Edward Broadbent consistently has been given much higher approval ratings in opinion polls than either Prime Minister Brian Mulroney or Liberal Party leader John Turner, although the surveys never have shown more than one in four voters in favor of having the New Democrats form a national government.

But the socialists, over the years, have prevailed on both Liberal and Conservative governments to adopt programs such as Canada's universal public health care system and measures limiting foreign ownership of Canadian companies.

The tactic for both contenders in the closely fought campaign for the election today is to capture the small and seemingly elusive middle in this province of 1 million, which has been starkly, and often bitterly, polarized for most of its history.

Bankers, entrepreneurs, affluent suburbanites and well-to-do grain farmers almost always have voted Conservative. But in the precincts on the North End of this industrial city where Jewish, Polish and Ukrainian immigrants settled, a radical political tradition has survived.

Although the prairie socialism owes less to Marx than it does to religious principles and a vision of the New Jerusalem on earth, for four decades voters in the North End elected lawyer Joe Zuken, who acknowledged membership in the Communist Party, to the school board and the board of aldermen, until he retired in 1983 at age 71.

Observers here say that Pawley's bragging about private investment in the province is typical of the kind of pragmatic style that socialist governments have taken on once they have won power. Although hard-liners in his party still talk about their Marxist dream of gaining control of "the means of production," Pawley is actively seeking buyers for an ailing bus manufacturing company and other money-losing companies owned by the government.

"The problem with socialism is that we all define it in different ways," Pawley said. His philosophical kin, he said, are men like Willy Brandt of West Germany and the late Olof Palme of Sweden. The pillars of Canada's prairie socialism, he said, have been strong support for universal medical care, government ownership of utilities and, more recently, the takeover of the province's automobile insurance.

When insurance agents bitterly opposed the program, the previous New Democratic Party government, in which Pawley had served as attorney general, found a pragmatic solution. They made the private insurers the agents for the new government program.

Pawley pulled Manitoba out of the recession with massive infusions of government funds for grants to small businesses, mortgage subsidies and loans to prop up shaky credit unions. Manitoba's gross domestic product grew by 4.5 percent in 1985, and unemployment was 7.9 percent, one of the lowest rates in Canada.

The centerpiece of Pawley's campaign platform is his plan for a major expansion of the provincially owned hydroelectric power utility. Last month, he announced arrangements to sell more than $3 billion in electricity to three consortiums of Midwestern U.S. power companies.

Although businessmen and bankers still support the Conservatives, they indicate that they do not believe it would be catastrophic if the New Democrats are returned to power.

"There's a lot of money being spent here now, and that is the best evidence to be had of improved confidence in the business community," Simon Kouwenhoven, a Bank of Montreal senior vice president, told reporters earlier this year as he complimented the socialists' efforts in pulling the province out of the recession.