President Reagan yesterday personally entered the battle to save his proposal for a free-trade agreement with Canada, telephoning wavering members of the Senate Finance Committee to appeal for support and telling all the members in a letter that withdrawing the plan would hurt U.S. relations with its northern neighbor.

A Finance Committee vote -- which could kill the plan -- is set for this morning and nose counters in the administration, on Capitol Hill and at the Canadian Embassy were unsure last night of the outcome.

Some administration sources predicted the presidential arm-twisting could give the free-trade proposal a one-vote victory, but others were less certain. Some committee members who last week sent a letter to Reagan urging him to withdraw the measure, yesterday refused to say how they will vote.

Along with the administration, tbe Canadians took an active role in lobbying. Ambassador Allan Gotlieb told The Wall Street Journal yesterday his country is likely to withdraw its offer to negotiate a free-trade pact with the United States if President Reagan fails to get the "fast-track" negotiating authority he is seeking. Under special rules for trade negotiations, the president gets that authority unless either the Finance Committee or the House Ways and Means Committee votes to disapprove it.

If the Finance Committee votes it down, Gotlieb was quoted as saying, "we will not see a Canadian government propose a similar initiative for closer trade arrangements with the United States for a couple of generations."

The president is seeking authority to bring a trade agreement to Congress for "fast track" consideration without any amendments. Opposition to giving Reagan what he wants exploded at a Finance Committee hearing earlier this month because of bipartisan frustration with the lack of an administration trade policy and a series of trade frictions with Canada.

The presidential strategy appears designed to gain support from committee members concerned with specific Canadian trade disputes. The most concerns are that Canada illegally subsidizes its forests in a way that has led to a surge of lumber imports in this countries. Other areas of friction include potatoes, fish, cattle and hogs.

Both Reagan and Prime Minister Brian Mulroney have a lot at stake in today's vote. They agreed to pursue a free-trade agreement at last year's "shamrock summit," and the proposal has become a cornerstone of Mulroney's economic policy.

Over the past year, however, increased opposition has developed to the idea in Canada, where provencial governments, which have more power than U.S. states, are seeking a major role in the talks.

The two nations have the largest volume of two-way trade in the world, totaling $116.7 billion last year.

"Opening the United States-Canadian borders will dramatically expand American exports, thereby creating thousands of new jobs," Reagan said in his letter to the 20 members of the Finance Committee. "Furthermore, opening borders will make the firms and industries of both countries more competitive internationally. . . .

"Failure to initiate these negotiations," the president continued, "would adversely color the tone of our political and economic relationships with Canada for many years to come. Allowing such an opportunity to pass could jeopardize progress in liberalizing the U.S.-Canadian trading relationship. . . . Further, Canada has been very supportive of U.S. international initiatives, particularly in combatting terrorism and maintaining a solid unity on major East-West and arms control issues."

Reagan added that talks to resolve trade frictions over Canada's lumber sales "already have been set back" as a result of the unexpectedly strong Finance Committee opposition.

The White House was joined in its lobbying efforts by influential business groups, including the U.S. Chamber of Commerce, the National Association of Manufacturers and the American Association of Exporters and Importers.