VISITING THE HORSES The stables are open for tours daily from noon to 4. Admission is free. Large groups should call ahead: 692-9593. Fort Myer is located at U.S. 50 and Pershing Drive in Arlington. Ask the guard at the gate how to get to the stables.

The cavalry no longer charges up the hill in battle but there are still 31 horses on active duty in the U.S. Army. They keep the caisons rolling along at military funerals and other ceremonies, and they receive visitors every day from noon to 4 at the Fort Myer stables in Virginia.

"This is Jimmy C., named after President Carter," said Specialist Brown, leading one adult and three child visitors through the stables. Jimmy C., a mixed appaloose recently acquired by the Army, is one of 15 white horses in the stable. There are also 16 black horses, but the colors have no moral significance. The white horses form one team and the black horses form another and they divide up the funerals, two or three of which occur every day.

White-horse tack - saddles and stuff- and black-horse tack are kept in separate tack rooms, even though it looks exactly the same.

"It's spit-polished every day," said Brown, one of 32 soldiers who polish, groom, hose down and exercise the horses and also ride in the funerals. The stable is hosed down every day and the horses are groomed every day. Before every ceremonial outing, the horses are led through a door marked "wash room" for a good scrub. They are so clean the stable doesn't really smell like a stable.

"This is Harvey," said Brown, opening the door of the stall on one of the White horses and introducing him to the children. "He's one of the gentlest horses I know with children," Brown assured an adult as Harvey endured the petting of three pair of hands.

In addition to the horses, visitors get to see the wagons. There's the Tally-Ho Wagon, a vintage coach of English origin that carries retirees around to review the troops at military retirement ceremonies, and the Marriage Carriage, a 19th-century brougham used to carry military brides and grooms from the chapel to the wedding reception.

"A lot of these things were given to us by the Smithsonian Institution because they knew we had a use for them," explained Brown.

Not so the flat black wagon that has a room practically to itself.

"That's the caisson used to carry Kennedy," said Brown. Caissons, he explained, were originally used to pull cannons around battlefields. When cannons became obsolete, the caissons were converted to pulling caskets. Six horses pull each caisson, three with riders and three without.

"This is a dummy casket - it's used for cremations," said Brown, pointing to an oak box with a barely perceptible trap door. The casket is placed on the caisson with the urn of ashes inside, but when it's time for burial the urn is removed and buried without the casket.

"This is a military tradition that goes back to the days of Genghis Khan," said Brown, leading his charges to a display of caparisoned tack. "Cap" tack, used at funerals of high-ranking officers and presidents, consists of the officer's saber and his boots, turned backward in the stirrups. In Genghis Khan's day, the horse got buried with its master to serve him in the afterlife. But at Arlington Cemetery, the tradition stops at the grave site.

"It would be too expensive to bury the horses - they cost an average of $900 each," chuckled Brown. The caparisoned, riderless horse who marched in President Kennedy's funeral, Black Jack, attracted a coterie of loyal admirers - one of whom used to bake him an oat cake on every birthday. Black Jack died in 1969, but others carry on the tradition.

Most of the black horses were out working a funeral the day of our visit, but a few remained in the barn. Some were being exercised in an outdoor ring next to the stable and some were just resting in their stalls.

"That's a Morgan horse - our only registered horse," continued Brown. "And that's Stardust. He's part Clydesdale and weighs 1,800 pounds. This is Oklahoma. He's the only horse I know who gives kisses."

Brown opened the door to Oklahoma's stall. Three little girls waited eagerly with upturned faces, but Oklahoma apparently wasn't in the mood.

"Back in 1957, the Army was going to give up the horses and just use hearses at funerals," said Brown. "But I guess they figured they needed to keep some traditions." CAPTION: Picture, THE WHITE-HORSE TEAM RETURNING FROM ONE OF THEIR SEVERAL DAILY FUNERALS AT ARLINGTON NATIONAL CEMETERY. By Ken Feil.