Yesterday, in her first inspection of a local facility that could develop into a first-lady project, Nancy Reagan went to the Rock Creek Park Horse stable and riding ring.

Finding a project to combine Nancy Reagan's interest in special education, children and horses would have been hard in any city but Washington. The Horse Centre has a special education therapeutic riding program, which is one of the few that use horseback riding to teach confidence, adn skills, to emotionally and physically handicapped youngsters.

"Are you "President Reagan?" cried out Sammy Klein, 10, one of the students from the Mamie D. Lee School, as Reagan walked onto the riding area. He didn't wait for an answer and almost knocked her down with a bearish hug. Reagan, who was warmly dressed in a brown coat, brown boots and black gloves, smiled and returned the embrace. After a few minutes of orientation, Reagan helped Donnell Chase, 10, onto his horse and chatted and petted the horse as they walked around the ring.

The centre was chosen for Reagan's first appearance at a local service project, said Sheila Patton, the first lady's press secretary, "because enough of us on the staff had heard about it or knew about it. It kept coming up." The private board of the centre, according to Alfred Edelson, the treasurer, had not been able to interest Rosalynn Carter in the program. "We hoped Mrs. Reagan's interest would cause other people to be interested," he said.

When she first walked in, Reagan said, "Oh, it smells good," according to Effi Barry, the wife of Mayor Marion Barry. She mentioned some homesickness for her ranch in California. During a brief private meeting with the program's director, Robert Douglas, they discussed the program's purposes, its sucesses and recent budget tightening. The program currently enrolls 250 students, instead of the 500 attending previously. The school is now operating on a federal grant of $36,000. To become a model program, said Edelson, the program needs to build a $1.2 million indoor facility and to have an annual budget of $500,000. Asked if he felt the Reagan administration's austerity would effect the future of the program, Douglas said, "My feeling is that since Mrs. Reagan knows the program works, that our funds will be increased."

Barry thought the hour-long trip had been beneficial. "It's good for the program to have that kind of national attention. Our positive programs need to be emphasized. She was very impressed."

Barry is planning a lunch for Mrs. Reagan in the spring, "to encourage her to be involved in local projects."