In an era when horse racing often consists of infirm animals running over frozen tracks to generate money for hard-pressed owners and greedy politicians, the morning scene at Hialeah Park's Barn AA is a total anachronism.

As the horses of Calumet Farm go through their daily routine, they evoke memories o what used to be the Sport of Kings. Their standard of living has not changed much since the winters when Whirlaway was stabled in this barn. It costs more for two horses to stay here each day than for two adults to stay at the Fontainebleau Hotel.

The sun already has risen past the top of the nearby now of palm trees, and activity at the barn already has begun, when trainer John Veitch arrives and surveys his operation. He notices at once that a colt named Damascus Silver is standing with his rear end to the door of his stall, an unsightly affront to the dignity of Calumet. Veitch pokes him on the tail. "Hey! Turn around!" Damascus Silver grudgingly obliges.

While the racetrack backstretch often appears a disorganized, chaotic place, Calumet preserves a touch of formality. On his doorway, every horse has a nameplate in the stable's famous colors, devil's red and blue, and outside is a red and blue feedtub. All the exercise riders wear red shirts, which Calumet buys for them.

The exercise boys and girls have been leisurely riding their horses around a walking ring for 15 minutes before Veitch arrives, and after another 10 he directs them toward the racetrack with an instruction for each. "Graham, walk to the quarter-pole gap and jog to the three-eighths pole... Charlie, jog him to the three-quarter pole and gallup back."

One of the horses stops, looks at Veitch inquisitively and nuzzles his hand, hoping for a lump of sugar.

"I've got nothing for you," the trainer says, with affection, for the horse is Alydar, who has contributed mightily to the resurgence of Calumet's fortunes in the last two years.

Veitch follows on fot as the horses go to the track, and here he watches them silently. This is his principal job in the mornings: watching.

"If a horse has run recently," he says, "you try to judge how much the race took out of him. You look at the mechanical things, how much life he's got, how bright the coat is."

The muscular chestnut colt passes by, his mind no longer on lumps of sugar.

"Alydar looks tremendous," Veitch says. "He's come back from his injury and he's still got his old enthusiasm."

After observing the first of four groups which will go to the track, Veitch walks back to the barn where activity is now in full swing. Grooms prepare to wash the horses who have just worked; exercise riders are preparing to get on their next mounts.

Only the dozen or so stable cats remain insouciant, presumably contemplating their good fortune in being adopted by Calumet and shipped here by air from New York for the winter.

As the second and third sets of horses go to the track, Veitch's con centration deepens. He is trying to catch a glimpse of the future. These are his babies, the Calumet 2-year-olds.

He can hope to experience the exciting sense of revelation that he did two years ago, when Alydar began to display his initial signs of aptitude and enthusiasm. But it is still too soon to tell.

Veitch looks at a young filly who is a half sister to Alydar and says, "It's as if your parents are Albert Einstein and Madame Curie and you're still having trouble with third-grade math."

By 10:30 a.m., the last of the 2-year-olds have come back from the track and the pace of activity at Barn AA has begun to decelerate. Calumet's 30-odd employes are finishing their daily labors.

"So few people can afford to maintain an operation like this," Veitch says. "It costs us over $50 a day for each horse. For that money, the horses get better grooms and exercise people, more supervision, more time out of the stall.

"At most outfits the exercise boys get up, go out to the track, come back and get right off. Here the horses walk 25 minutes before they go out, and another 40 minutes after they come back. This afternoon they'll be taken out of the stalls again, walked and grazed.It all pays off. With horses of this quality, this is the only way to do it."

If that filly by Albert Einstein out of Madame Curie should be blessed with great potential, she has found the right environment in which to develop it.