Ronald Wilson Reagan, beginning his second term as president of the United States in weather so severe that for the first time in history all outdoor inaugural events were canceled, appealed to citizens yesterday to join him in "creating a new America."

"There is always a better tomorrow," he said, standing inside the Capitol Rotunda and expressing a theme of optimism tempered by the necessity of making what he called "hard decisions" over freezing government spending, reducing the budget deficit and gaining an arms-reduction agreement with the Soviet Union.

His Inaugural Address, delivered from a podium directly under the great cast iron Capitol dome towering 183 feet above, was a call for an American renewal and a restatement of his determination not "to reverse course" from the direction he set four years ago when he became the 40th president.

"My fellow citizens," he said, "our nation is poised for greatness. We must do what we know is right and do it with all our might. Let history say of us, these were golden years when the American Revolution was reborn, when freedom gained new life, when America reached for her best."

None of the 49 previous inaugural ceremonies had been held there. None took place under such harsh conditions.

As he spoke, he was surrounded by a select 1,000 witnesses out of the 140,000 who had expected to attend the formal ceremonies on the West Front of the Capitol overlooking the memorials along the Mall. Outside, Washington lay locked in the frozen grip of record-low temperatures.

Earlier in the morning it had been 4 degrees below zero and the wind chill factor was 25 below. Inaugural officials, in announcing cancellation of outdoor events, spoke of the dangers posed to "exposed flesh" by the numbing cold.

They were especially concerned about the prospect of the 10,578 Inaugural Parade marchers -- many of them teen-agers -- suffering frostbite or worse. The arctic blast that swept into Washington with devasting impact was part of a front that dropped temperatures to 27 below in Chicago and shattered record after record as it moved across the country.

Instead of a bustling capital that expected to be host to a million inaugural visitors and residents cheering the president along the traditional parade route, Washington yesterday resembled a ghost city.

The president's procession from the White House to the Capitol for the official ceremonies, which began at 11:11 a.m., was one unlike any that preceded it: All along the route, Reagan's limousine carrying his wife, Nancy, and other officials passed rows of vacant bleachers. Hardly anyone was out.

Physically, Washington never looked finer. The city sparkled under a hard bright sun and cold blue skies. The snow-covered grounds about the White House and Capitol glistened, as did the familiar white marble monuments. But the streets were deserted.

These conditions, which always will be identified with Reagan's second inaugural, gave the ceremonies an unusual air of intimacy. His address, delivered without the use of TelePrompTer in a place more familiar as the one where former presidents and national heroes from Lincoln to John F. Kennedy have lain in state, was vintage Reagan.

The president began with extemporaneous remarks welcoming back to political service Sen. John C. Stennis (D-Miss.), who has been recovering from the amputation of his leg. "This day has been made brighter" by Stennis' return to Congress, he said.

Then the president took note of "one not with us . . . who left us last night." He was referring to Rep. Gillis W. Long (D-La.), who died Sunday night of a heart attack at the age of 61.

In his speech, which he read in a conversational tone, his words echoing throughout the packed chamber, Reagan urged action to reduce the national debt, promised to submit to Congress "a budget aimed at freezing government program spending for the next year" and received his greatest applause when he said:

"Let us make it unconstitutional for the federal government to spend more than it takes in."

He made clear that he intends to press for increased American defense capabilities, saying "much remains to be done."

He also pledged to work for an arms-reduction agreement with the Soviet Union, appealed for support for his controversial "Star Wars" plan to develop "a security shield that will destroy nuclear missiles before they reach their target" and said:

"For the sake of each child in every corner of the globe, we seek, one day, the total elimination of nuclear weapons from the face of the Earth."

The ceremony concluded at 12:14 p.m. with the singing of the National Anthem. Reagan, two weeks away from his 74th birthday and the oldest president, sang with his wife beside him.

Outside, the sound of the traditional 21-gun salute echoed over the Capitol grounds and was clearly heard inside. Then, after a brief moment of picture-taking with his wife, Vice President Bush and Bush's wife, Barbara, the president waved to the group and left for a luncheon in his honor at the Capitol as the Marine Band played "Hail to the Chief."

Reagan's second Inaugural Address was hailed immediately for its bipartisan tone, even though politicians of both parties predicted that he would have difficulty achieving all of his ambitious agenda.

Typical of the Democratic reaction was the comment of Sen. Joseph R. Biden (D-Del.), regarded as a potential 1988 presidential candidate. Biden pronounced Reagan's speech "brilliant . . . optimistic, exciting" and compared it to Kennedy's Inaugural Address 24 years ago.

That tone of optimism was reflected in the reaction of Wall Street.

The stock market soared. The Dow Jones industrials closed 34 points higher. It was the largest increase since Jan. 19, 1984, when Reagan set out to seek to become the first president elected for two terms since Richard M. Nixon in 1972 and the first full eight-year president since Dwight D. Eisenhower.

The inaugural ceremonies this year were marked by another historical oddity. Since the constitutionally prescribed date of Jan. 20 fell on a Sunday, the president chose to take the oath in a small White House ceremony and keep the formal celebration with parade and panoply for Jan. 21.

Those hopes were dashed by the bitter weather that led to the decision Sunday night to cancel outdoor events.

It was a decision that left trivia buffs scrambling for their record books and countless thousands sorely disappointed. They had traveled from across America, many at great personal expense and all with high expectations of witnessing history, only to find it was for no avail.

The historic precedents were quick to find: Reagan's second Inaugural Day was colder even than Ulysses S. Grant's in 1873 when the temperature hovered at 16 degrees and, it was said, canaries in outdoor cages froze to death. Why the birds were there is a mystery the buffs have yet to resolve. Not since 1909, when a howling snow storm forced William Howard Taft to take his oath indoors, had an inaugural ceremony been held inside. Taft's Inaugural Parade, though, continued on schedule with the new president braving frigid winds as the bands and floats moved past him in front of the White House. Only once before, in 1833 when Andrew Jackson came to office, had inclement weather forced other inaugural ceremonies inside. But never had all such events been canceled.

No amount of historical rendering of inaugural precedents could assauge the feelings of hurt and disappointment on the part of so many. When the word came that the parade had been canceled, there were tears and sobs from young members of band troupes.

Many of them had practiced late into the chill night on Sunday and planned to begin assembling at 4 a.m. on Inaugural Day for their march. They greeted the news of the cancellation with disbelief and sorrow. Some continued practicing, as if their activity would somehow produce a reprieve. It did not.

Their disappointment was heightened by special circumstances that brought them to this inaugural.

Unlike other Inaugural Parades that dragged on for hours and ended in darkness, this time the inaugural committee was determined to stage the parade to last only 1 hour and 15 minutes.

As a result, only one unit was chosen to represent each state or territory. Thus, competition in each state was unusually sharp. Equestrian units were selected in similar fashion. Then, after being picked, each of the 112 units scheduled to participate had to raise the money to get here. No funds were provided by the inaugural committee.

Television, the ubiquitous electronic cable that linked Americans everywhere directly to the scenes in the capital, recorded groups of teen-agers hugging each other and offering words of consolation after they learned that they would not be able to participate in an event for which they had practiced so long.

Others, depending on background, circumstances and political views expressed different reactions -- and some of them bitter.

An aide to a southern Democratic governor, after the governor was told by inaugural officials shortly before midnight that he should cancel his plans to fly to Washington with his family for the ceremony because "there was no room for him" inside the Capitol Rotunda, saw this as a form of political-enemies list.

Others, who had paid big sums for travel and hotel accommodations, were out of pocket -- and out of sorts.

But none of that seemed to matter later when the Reagans and Bushes traveled by helicopter to the Capital Centre in nearby Maryland. There, the parade groups had assembled to pay the president tribute.

Whatever disappointment they had felt earlier seemed to dissipate quickly when the president spoke to them. He apologized for the cancellation and expressed regret at the severity of the coldest inauguration in American history. But nothing, he said, could diminish the warmth of their welcome.

He was greeted with cheers and screams as he called out the names of states from Hawaii to Texas and then on to the East Coast ones that had sent delegations to march in his parade. He had elicited the same wild cheers when the roll was called of delegations to last summer's Republican convention, which was held in record-breaking heat in Dallas.

This time, in record-breaking cold, the cheers were at least as enthusiastic as they had been in the suffocating heat of summer.