By night, Frank Sinatra and Tom Selleck entertained the bankers and businessmen, the politicos and others who are the Republican Party now. But the day belonged to the future, as GOP stalwarts wooed the young yesterday in an unprecedented round of inaugural activities designed just for them.

The Republicans pulled out rock 'n' roll music, military bands, astronauts, a member of Congress and Vice President Bush in a multi- media pitch to win the hearts and minds of the young, who voted in large numbers in November for the oldest president in the nation's history.

On the second day of festivities in this 50th presidential inauguration, the party sought to cement the loyalty of the 18-to-29-year-olds, who handed President Reagan nearly 60 percent of their vote and whose continued support is crucial to the GOP's future.

"As long as you are with us, we are going to maintain power," White House aide Craig Fuller told a cheering throng of 2,000 budding Republicans who streamed into Constitution Hall for the Leadership Forum for Young Americans.

Yesterday's inaugural activities culminated with President Reagan's inaugural gala, which drew a capacity crowd of 12,000 persons to the D.C. Convention Center. The gala also drew a handful of pickets who carried placards protesting the fur coats worn by many of the women guests. There were no arrests.

President Reagan is to be sworn in for his second term at a private White House ceremony at noon today, the date mandated by the Constitution. But by tradition, the official public ceremony is delayed until Monday, when Reagan will take the oath again on the West Front of the Capitol.

About 140,000 guests have been invited to the ceremony on a day when weather forecasters predict frigid temperatures that would make it the coldest inauguration in 50 years. The National Weather Service is predicting a noontime temperature of about 15 degrees.

Even though he did not attend the Constitution Hall event, the president nonetheless was the star of the show, appearing in 10-foot color images in a rousing slide show depicting Reagan at the space shuttle, Reagan at the Olympics, Reagan with Michael Jackson and Reagan with happy young people.

The young people broke into spontaneous cheers and applause at Reagan's smiling image, but several blocks away another predominantly young crowd shouted his name derisively in a march protesting Reagan's policies, led by the Rev. Jesse Jackson.

At Constitution Hall, the clean-cut and well-dressed young people, who came from across America with their families, were treated to inspirational songs and speeches thanking them for their vote and asking their continued support.

Last night, planners had arranged for the rock band Kool and the Gang and rock 'n' roll great Jerry Lee Lewis to entertain young people at the D.C. Armory.

But the youths so attracted to Reagan at election time didn't turn out in record numbers Saturday night to celebrate that victory. Fewer than half the armory's 10,000 seats were filled for the two-hour show.

The mood of the crowd was focused on the inauguration -- but not the inaugural event before their eyes. When country star Johnny Lee Lewis started a foot-stomping rendition of "Billy," few of the feet in the crowd moved.

Some of the young embraced the ways of their parents in more than philosophical terms Saturday night. Furs and pearls and sequins and diamonds were in fashion last night for everyone from 14 to 40.

For many the chance to participate in an inauguration was an exciting culmination to several years of political activism.

"I was absolutely in awe and got goose bumps when that band came on and Vice President Bush came in," said Stacey Sickels, 18, a Sweet Briar College freshman and the daughter of a vice president of Duron Paint, who attended the earlier activities at Constitution Hall.

For political strategists, conventional wisdom used to hold that winning the support of a first-time voter was akin to winning his or her loyalty for life. But not so anymore, judging from the comments yesterday of young Republicans who said their attraction to the party was inherited from parents but that they would not necessarily vote GOP for the rest of their lives.

"This was my first presidential vote, but I don't vote party lines," said John Carr, a 20-year-old student from Salem, Ore.

"I credit the '60s movement for opening the eyes of our generation," said his 21-year-old classmate Todd Imhof. "We are better educated about our vote. I voted for a Democrat for governor, and still voted for Reagan-Bush. I don't care, if someone can lead the country, whether he's a Republican or not."

Nearby, a die-hard Republican at age 22, Joseph J.E. DeShane sported a black bow tie, a Reagan-Bush pin on one lapel and a Harvard University pin on the other.

DeShane, son of a retired career Navy officer "who taught me what communism can do," said he aspires to a job with the State Department and calls himself "a yuppie," referring to young, upwardly mobile professionals.

Criticisms that Reagan is insensitive to the poor have "disturbed me greatly," DeShane said, adding, "I think those criticisms are extremely exaggerated." He said he worked in a Boston area soup kitchen last year and met a number of poor families who were forced to accept charity because of Reagan's cuts in the food stamp program.

At the Constitution Hall gala, Bush, in what sounded like a vintage campaign speech, said, "The hope for the future is not more and more government, but more and more opportunity for all Americans . . . . We believe government is to serve people, and not the other way around."

After remarks by astronauts Joe Allen and Anna Fisher, Rep. John G. Rowland (R-Conn.), elected as the youngest legislator in Congress at 27, told the crowd, "You are the most important group here . . . . You have shown it is possible to build a new America around a new consensus."

Young people today, he said, are "no longer burning flags . . . no longer preaching negativism, no longer damning authority." The reason, he added, is "the person we'll be swearing in as president Monday."

Robin Green, 26, a staunch Republican who works for Sen. Phil Gramm (R-Tex.), brought her roommate, Jackie Webster, 24, a Democrat. "I grew up with older brothers during the Vietnam years, with the disillusionment about government in general and Republicans in particular," Webster said. "I'm surprised young people have completely turned around . . . . If they can get out of college and get a job, thanks to Reagan, they're not interested in any other issues."

At the program's conclusion, Imhof said he "loved the optimistic feeling" in the big hall, and said young Americans do not want to hear "pessimistic predictions" about the future. "We want to hear that it's going to be a bed of roses," he said, "even though we know that it might not be true."