Since Christmas, Canadians have switched from worrying about the possibility of a prolonged and disastrous recession to wondering how viable the expected 1983 recovery will be.

Like the U.S. economy, to which it is inextricably tied, the Canadian business climate is showing enough weak but persistent signs of improvement to convince many economists that the worst is over.

But there are a number of imponderables, not the least of which is the threat created by the shaky oil market. Oil and gas activity are being counted on to support the recovery.

In any event, it will be an uphill climb. Last year Canada's output fell by a shocking 5 percent, reflecting a crisis unknown in half a century in this resource-rich nation. It was also by far the worst decline of any industrialized country.

The uncertain economic outlook confronts Prime Minister Pierre Trudeau's Liberal government with a difficult choice.

During the winter, a consensus emerged that Ottawa, despite a government deficit that has ballooned to almost $25 billion in the current fiscal year, might have to spend more to stimulate the badly-battered economy.

But with signs of a recovery apparent, the wisdom of such a move is once more being widely questioned by those who fear renewed inflation and rising interest rates if outlays and the deficit rise.

"Given the size of the deficit that's already there, it doesn't make any sense to pile on any more," said Laurent Thibault, executive vice president of the Canadian Manufactures' Association.

Trudeau's finance minister, Marc Lalonde, will have until April, the date of a promised new budgetary message setting out the country's economic program, to make a decision. He is to meet shortly with Canada's 10 powerful provincial governors to discuss strategies for repairing the business climate.

In its most recent forecast, the highly-regarded Ottawa-based Conference Board of Canada research group wrote:

"Even though the nation has emerged from its recession and the economy will continue to expand throughout 1983, the long, steep decline suffered last year has left the economy at such a low ebb that considerable growth will be required merely to raise activity to the average level of 1982."

William Mackness, chief economist at the Bank of Nova Scotia in Toronto, adds, "The recovery is not guaranteed, but it is definitely launched."

He said the driving force now is coming from companies replacing depleted inventories, a trend that is happening, he said, at a much stronger pace than after any recent business downturn. "Literally, there is nothing left in the pipeline. You can read it on both sides of the [Canada-U.S.] border in new orders and in a firming of employment," he said.

But most economists agree 1983 will not be a year of superlatives. Gross national product, the measure of Canada's goods and services, is expected, when discounted for inflation, to show growth of only about 1 percent.

There will likely be important improvements in consumer prices (predicted to increase at only about 7 percent this year compared to 10.8 percent in 1982) and interest rates (with the banks' prime rates likely to stay near the current 11 to 12 percent range, down from a peak of 20 percent in 1981).

Now that borrowing rates have eased, manufacturers and small businesses are reporting a modest but noticeable upturn in orders and sales.

Economists predict improvements in key sectors, such as the forest industry, mining, autos and retail sales. Housing starts estimated at between 140,000 and 150,000 this year would represent a 15 percent increase over 1982, but still would not be a strong performance.

The big question is consumer spending. With unemployment continuing at 12.8 percent -- the highest level since the Great Depression -- worried consumers husbanded their funds even more stringently than usual. Last year, Canadians increased their savings rate to 13 percent from 11 percent while Americans put less than 6 percent of their after-tax income in the bank.

Alberta, the western Canadian province with plentiful oil reserves, is expected to lead Canada in economic performance. With oil and gas activity forecast to pick up in 1983, the province's real growth in output will be above 2 percent.

And the expected upturn could be crushed by a slide in world petroleum prices, which would cause further damage to an industry already hurt by Canada's nationalistic energy policies.

Offshore exploration for oil and gas beneath the Atlantic will boost economic output in the eastern Canadian province of Nova Scotia by 2 percent-plus this year.

But growth will remain weak elsewhere, particularly in the two most populous provinces, Ontario and Quebec, which have suffered severely from slow activity in the country's manufacturing industries.