President Ronald Reagan often rides a brown U.S. Park Service thoroughbred named "Jackpot" on his occasional outings through Rock Creek Park or Quantico Marine Base. But for the recent visit of King Hassan II of Morocco, the president wanted a horse of a different color.

His choice for the king? Two Lippizaners, the white horses originally bred in Austria and known to the world for their balletic maneuvers. Hassan cantered across the the Virginia hills on a gelding named "Pluto III Reseda," great-grandson of the Lippizaner stallion "Pluto XX" given to Gen. George S. Patton by the Spanish Riding School in Austria.

The two Lippizaners are Army horses, part of a herd of 10 donated a year ago to the Caisson Unit at Fort Myer by a steel magnate in Chicago. They usually pull caissons at military funerals and perform other ceremonial duties and had never been put through presidential paces. Reagan heard about the horses and asked to see them after a recent ride at Quantico. The Army obliged and shipped the horses from Fort Myer for a presidential inspection, which they apparently passed.

Wednesday's ride lasted less than two hours and took place on Fairfield Farm, the 4,500-acre estate owned by the Marriott Corp., the hotel and restaurant chain. J. Willard Marriott Sr., who has a home on the Hume, Va., estate in the Blue Ridge Mountains, had extended an open invitation to the president for its use.

The president and the king rode with National Security Adviser William P. Clark as well as an unspecified number of Secret Service agents riding customary park police mounts. The president's physician was also on hand, the White House said.

Neither the king nor the president commented about the ride, which was captured in a newspaper photograph showing the king's horse ahead at an extended walk, while the president's mount had its head back and appeared to be balking. "That's because the president had just stopped his horse," explained Peggy Raines, an employe at the Marriott farm. "He had no trouble controlling his horse."

In fact, equestrians consider the president to be a capable horseman. "He's a very good rider," said Michael Nolan of the American Horse Council, "and he'll ride in the damnedest weather." Nolan said, however, that the president has not turned out to be a champion of the horse industry.

"We were thrilled with the idea of a horseman in the White House," said Nolan. "But so far, his Interior Department has cut funds for horse trails, and a variety of things. So really, there has been very little impact."

Not everyone agrees with that assessment. "He's done a lot for the industry," said Gary Lashinsky, producer of a Lippizaner show that tours the nation. "Every time Mr. and Mrs. America see the president on horseback, they think, 'Hey, why don't we try that.' " It's almost as good, said Lashinsky, as "the queen and Prince Philip in England."