President Ford is beginning the new year in a mood of relaxed optimism and a conviction that he will remain a force on the political landscape lfor a long time.

Ford will leave the White House on Jan. 20, but he has repeatedly expressed the belief to aides and friends that he will continue to be a factor in public life. During the past week he has been making proposals that either cannot be accomplished during his presidency, such as Puerto Rican statehood, or might more fittingly be left to his successor, such as gasoline price decontrol.

Part of the reason for these proposals is Ford's determination to function as President until the day he leaves office. But those who have seen the President at close quarters during his happy vacation here think that the reasons for Ford's activism go beyond a final show of presidential power.

More revealing than any specific proposal is Ford's frequent reiteration of the sentiment he voiced last week on the ski slopes: "I'll be around." Though Ford is disinclined to be a critic of Jimmy Carter during the latter's honeymoon period as President, Ford expects to be called upon to express Republican positions on a variety of issues during 1977.

He was, in effect, making such a statement Saturday when he proposed Puerto Rican statehood, which is a tenet of the GOP platform approved in August at Kansas City.

One of the signs that the President is looking ahead, both personally and politically, is that he is no longer second-guessing the missed opportunities of the 1976 campaign. The melancholy induced by his election defeat is gone, and Ford is now talking about his future, not his past.

That future is bright, Ford has received hundreds of offers to speak or lecture, some for as high as $5,000 a speech. Even without the $100,000 a year he will receive from congressional and presidential pensions, Ford is assured that he never again will have to worry about making a living or providing for his family.

At first, during the period coinciding with the anticipated Carter political honeymoon, Ford as ex-President will divide his time between playing golf in Palm Springs, Calif., and skiing in Vail. But he is expected to announce later this month his plans to lecture at the University of Michigan, his alma rater, and to "write a book that will stake out Ford's claim as a continuing political spokesman.

Ford's final week of travel as President has contrasted starkly with the last presidential trip of his predecessor to San Clamento, Calif., 3 1/2 years ago.

At that time, Richard Nixon, fearful and despondent, isolated himself and sent out his press secretary to denounce criticed news accounts and tell reporters that he would never be impeached by the House.

Ford'd press secretary left Vail the day before Christmas and the President has been meeting daily with reporters on his way to the ski slopes. He also has gone out of his way during his two weeks here to seek out staff members, reporters and friends and express his personal appreciation for their efforts.

Ford is, in fact, far more accessible and outgoing than he was at Vail a year ago, when he was troubled by White House pressures and the pending primary challenge of Renald Reagan. Except for two football-watching days on this trip, Ford has skied long and enthuastically on Vail's slopes, which were patchy at first but have improved under a year-end snow.

He spent evenings making the rounds of parties held for him by local businessmen, the White House communications agency, the Delta Keppa Epsilon fraternity and the White House press corps.

On New Year's Eve the Fords hosted a party at their rented chalet and invited several correspondents and their spouses to see in the New Year.

The only sour note of the week, as far as the President was concerned, was the publicity given his remarks on amnesty after he telephoned Jane Hart to express condolences on the death of her husband, Sen. Philip A. Hart (D-Mich.)

Ford politely asked if there was anything he could do and Mrs. Hart, an antiwar activist, asked him to grant amnesty to Vietnam war evaders in her husband's memory. The President said he would look into it.

Resulting news stories, prominently played in some publications, suggested that Mrs. Hart's request might become reality. This seemed overdone to the President, who knew that reporters were well aware of his consistent opposition to a blanket amnesty plan. Ford was even more embarrassed by a second round of stories that seemed to him to indicate that he had been insincere in saying to Mrs. Hart that he would re-examine the issues.

When a television reporter pressed him about it after one of his skiing outings, Ford's temper flashed and he accused the reporter of wanting to manufacture something out of nothing.

Some reporters here agreed with Ford that the story had been exaggerated. But they also were reminded of the difficulty that Ford has always had in extricating himself from his own will-intended but inexpert sentences, most notably when he refused for two days after the second presidential debate to correct a statement saying that Eastern Europe was not dominated by the Soviet Union.

"The President's a stubborn man," said one aide. "He knows what he meant to say and he finds it difficult to apologize if he thinks people are nit-picking his words and ignoring his meaning."

But Ford's annoyance passed as quickly as it came. The next day he cheerfully delayed his skiing to hold an impromptu news conference on the mountain. When the television reporter who had first questioned him about amnesty said that he hoped the President would talk about something else because "we're tired of amnesty," Ford replied with a smile: "If you don't ask me any questions about it you won't get any answers."

The President has been enjoying himself at every excuse at this last, relaxed presidential vacation, and his mood was especially cheered by the year-end snow.

That long awaited snow was as welcome in Vail as the cavalry in a western movie. Businessmen here would have faced a dismal winter if the dry spell had continued into January. The snow was even more welcome on the parched Western rangelands, which depend on snowfall for a significant portion of their year-round moisture.

Now the snow has brought a happy new year and a beginning to the West. And on the last day of his last trip as President, Ford looked symbolically forward to his own beginning on Jan. 20, serene in the confidene that he was well thought of by those who knew him best.