Pianist Vladimir Horowitz, 81, who left his native Russia 61 years ago vowing never to return, announced plans Thursday to play two recitals in the Soviet Union this spring. "Before I die, I want to see the country in which I was born," Horowitz said. "But I didn't want to go home as a tourist. I wanted to play."

The first concert is scheduled for April 20 at the Bolshoi Theater in Moscow and the other a week later at Leningrad's Shostakovich Hall. They are a result of renewed cultural exchanges between the United States and the Soviet Union arranged at the Geneva summit in November between President Reagan and Soviet leader Mikhail Gorbachev, said Horowitz's manager, Peter Gelb.

Horowitz left the Soviet Union in 1925, in a postrevolutionary period of hardship. In a 1980 interview, he said, "I have no desire to return. I don't like the Russian approach to music, to art, to anything. I lost all my family there. I never want to go back and I never will."

Asked Thursday if he considered himself an American cultural ambassador or a Russian returning home, he quickly replied, "I am an American. I have lived here for 40 years -- longer than in Russia. This is my home." Taking a Peaceful Stroll

Thousands are expected to participate in "The Great Peace March," a walk from Los Angeles to Washington, D.C., to show support for worldwide nuclear disarmament. The walk, sponsored by an organization called PRO-Peace, will kick off March 1 with a send-off ceremony at the Los Angeles Coliseum. PRO-Peace spokesman Peter Kleiner said yesterday that entertainers Paul Newman, Barbra Streisand and Elizabeth Taylor have been confirmed as cohosts of the opening ceremony. The participants are expected to arrive in Washington in November. Billboards From the White House

The first of what will be 4,000 his-and-hers billboards featuring Ronald and Nancy Reagan endorsing their favorite causes have been unveiled in Indianapolis.

"The response has been tremendous," said David Blackmer, spokesman for Kiwanis International, the Indianapolis-based civic organization that will put up the billboards across the nation. "I can't think of any other persons that we could have had the same response."

The billboards, placed side by side or stacked on top of each other, focus on drug abuse prevention and community food programs. The president endorses Operation Share & Care, a national private-sector campaign to increase public support for local food banks and meal programs. The billboard says, "Support community food programs. Volunteerism makes a difference." Nancy Reagan's sign reads, "Help save a generation of children. Fight school-aged drug abuse." End Notes

Pop singer Ricky Nelson, who was killed in a plane crash on New Year's Eve, left his entire estate to his four children and specifically willed nothing to his former wife, his fiance' or his mother, Harriet Nelson. The court papers make no estimate of the value of Nelson's estate . . .

Katharine Hepburn escaped injury yesterday in a minor traffic accident on the Connecticut Turnpike, state police said. The actress, who has a home in Connecticut, was a passenger in a car that was involved in a four-vehicle accident on a bridge, officers said. There were no injuries . . .

Tenor Placido Domingo was released Thursday from a Barcelona hospital after undergoing an operation for a double hernia. Domingo said he "felt great," but he was, of course, unable to conduct, as scheduled, Thursday evening's gala concert at London's Royal Albert Hall, which was attended by Prince Charles and Princess Diana . . .

It's not quite a majority-rule campaign, but 68 members of congress, including House Speaker Tip O'Neill and Senate Majority Leader Robert Dole, will be seen on national television doing public service announcements to bring attention to osteoporosis, a bone disease that plagues more than 15 million Americans . . .

Singer Olivia Newton-John and her husband, actor Matt Lattanzi, are the proud parents of a healthy newborn baby. Newton-John gave birth yesterday morning to her first child, a 6 1/2-pound girl named Chloe . . .

It seems Billy Carter, former first brother, has finally found his niche. He has gone into business for himself, developing plans for a group of mobile-home dealerships. Carter said he plans to open dealerships in the Georgia towns of Columbus, Americus and Manchester and hopes to expand to other areas of Georgia and the South. Carter spent five years working for mobile-home and housing building companies, so he should know the business.