As lanky Wayne Carroll rides into the zoo, the tap-shoe clip of his horse draws a leopard suddenly from camouflage. Nostrils high, the two animals pace on either side of a chain link fence, the cat with his haunches low and his neck flat, the horse with his knees nervously brisk.

Above, a small boy spins away from the white swelter of the polar bears and glances only briefly at the leopard. "Hey, mister!", he calls. "Can that horse run?" And, smiling, Carroll lifts Tartagnan into a brief trot.

"Wow!", breathes a young girl, oblivious to a seal's bark behind her. "I've never seen a real live horse before."

Carroll slows, introduces Tartagnan, tips his hat and moves on, all the while scanning the parking lots and the straggling gawkers for the furtive motion of a pickpocket. "Look," says a teen-ager. "He's got a gun."

Carroll, 35, is a U.S. Park Police mounted officer, a walking, trotting police paradox of the Eighties: part of an elite force (40 officers in the Washington area), a legacy of the great American spaces, which some see as an urban law enforcement tool of the future.

"This is the way to get the police back into the neighborhoods," says Sgt. Denis Ayres, 50, the department's eminence grise and a superb seat. "In New York, they've taken the horses out of Central Park and put them all in Bedford-Stuyvesant."

These are, in a sense, the people's police: hands-on, visible symbols of the law in the places where city dwellers go to be free, the parks, the C&O Canal Towpath, and at the monuments and museums where the nation's pilgrims come to perceive their freedom.

In an era when the street cop suffers an unsympathetic stereotype, the mounted policeman is approached and admired, the last of the lawmen--a kind of Marshal Dillon of the Mall.

"It's an American tradition," Ayres says. "If you sit out in front of a hotel, everybody who walks by will tell you he can ride a horse. But if you ask if he plays golf, he'll tell you the truth."

In the Washington metropolitan area, the mounted park police--five sergeants and 35 privates--patrol a sweeping 57,000-acre crescent from Rock Creek Park and Seneca down the Great Falls parks, Glover Archbold to the Mall to Fort Dupont in Southeast, plus the Fort Hunt area below Alexandria.

They are primarily a deterrent force, most valuable in residential neighborhoods, where they can tap the front-porch gossip networks, and in crowds and parking lots, where their mounted height gives them a head start over petty thieves.

"And lovers and dope smokers and nude bathers," says Carroll, who patrols upper Rock Creek Park while training new horses. "You wouldn't believe what you stumble on some days."

In the wooded areas and jogging paths, the officers' syncopated presence ("I ride the beat a little differently every day," says towpath patrolman Bill Thomas) is designed primarily to deter assaults and rapes.

"They don't hear you coming," says Thomas, 37, ducking spider webs and summer vines in a pinwale path from the canal to the river's edge. "I rode up to the rocks one day where a woman was sunbathing and this guy just popped straight up out of the woods."

Sometimes they don't even see you coming, says Tony Taylor, 37, who has ridden on the Mall for a decade. "I don't know how," Taylor says, shaking his head, but an oblivious pickpocket once stole a $5 bill practically under the horse's considerable nose, then took off on foot as Taylor pursued on horseback.

"I chased this guy up and down 14th Street, and finally I said, 'Hey, I can run all day. Can you?' "

Horse and rider, usually paired for years, develop a mutual regard. Thomas, slipping off Royal Spokesman above the Old Angler's Inn on MacArthur Boulevard, says, "We've been together five years. I know when he needs a break."

"He isn't just a mount, he's a pet," says A. D. Smith, 39, who brings Caisson an oatmeal-raisin Tasty Kake every morning. "My wife says, 'You think more of that horse than you do of me!' . . . Eight hours a day, I do."

With the professional partnership comes a kind of character merger. Thomas, a long-distance runner who calls his sprawling beat "probably the most physical in the department," speaks with pride about his thoroughbred's speed and stamina. Smith, a rumpled strawberry blond, says the playful Caisson "thinks he's a lap dog."

So many horses are donated to the department that Ayres hasn't had to buy a mount in seven years. New recruits, both human and equine, endure 480 hours of intensive training. Like rookie cops, raw horses are paired with experienced mounts before graduating to solo duty.

"Some of them are race horses or cross-country hunters," Ayres said. "Basically, you're taking a horse from a rural environment and turning him into a city boy."

From the Rock Creek training barn, where they can be gradually accustomed to bikers and joggers and drainage grates, to Georgetown, with its major thoroughfares and barking dogs, down to the Mall and its monuments, the horses pursue a southerly course to veteran status.

"A good horse is made downtown," Ayres says. "We teach them the fundamentals at the barn . . . but when you can drop the reins at 17th and K, you've got a good police horse."

As police work goes, the officers say, riding a beat is the good life. "I didn't know anything about horses," says John Nelson, 36, mounted like a statue in Dupont Circle. "I just like dealing with people on a one-to-one basis."

"I got into it mainly to get away from the midnight shifts," admits Taylor, who, like all applicants, had to serve three years in a cruiser. "But I love it now. I know everybody down here--I'm a fixture."

As seductive as the job can be, there are serious moments. "You can't believe how cold it is in winter," Carroll says. In summer, the uniforms turn clammy and pungent. Even worse, some of the parks require frequent death duty, especially Great Falls, where climbers and bathers die each year despite the many posted warnings.

And there is the high-adrenalin duty of political demonstrations. Horses are a primary force in crowd control because people traditionally have given way to them. "I've been in all the major demonstrations of the past 25 years," Ayres says, "and never had a horse injured. People would throw things at us, bottles and rocks, but you'd hear them yelling, 'Don't hurt the horses!' "

In recent years, however, protesters have become more callous. Royal Spokesman still bears the scars of a brick-tossing, anti-Klan crowd. "I was splashed with gasoline during a big Iranian demonstration," Ayres says, "and I thought any second we were both going up."

Despite poison ivy and protesters, once mounted, a policeman tends to stick in the saddle, even though Park Police rules demand that an officer change departments if promoted.

"This is like dyin' and going to heaven," says A. D. Smith, gesturing up the towpath from the parking lot of Fletcher's Boat House. "I've had back surgery twice already, and they tell me I'm crazy, but I wouldn't transfer back to a car unless the doctor told me my life depended on it."

"I took the promotion exam," Nelson says, "but I took my name off even before the interviews. I figure, you only go through life once, and if you've got a job you enjoy, why even take a chance on losing it?"