RECENTLY our Close to Home page carried an account of the tribulations of Alan Fisk of Poolesville, whose local zoning authorities have barred him from keeping a pet sheep named Buttercup at his home. Mr. Fisk may not know it, or find it very consoling if he does, but he is part of a distinguished company of pet owners with zoning problems, some of them decidedly more offbeat than his.

For instance, consider Patty Fairchild, a Californian who spent the summer fighting an eviction notice served by zoning authorities upon her 27-inch-high horse. This (truly) 27-inch-high horse named Ragtime runs around Mrs. Fairchild's back yard and curls up in her living room -- she says -- to watch television. The neighbors say Ragtime is a farm animal and can't be kept in a suburban tract home. Mrs. Fairchild retorts that Ragtime is smaller than some dogs, is clean, is quiet and is a pet. "She'll lose," sadly predicts Mary Culbertson of the American Miniature Horse Association, who had a similar problem herself a few years back. "People just can't get past the idea that it's a horse." Either that, or it just gives them the creeps.

It is not at all clear that enough people are getting the creeps with reference to this new boom in miniature-animal collecting, which encompasses, these days, not only horses and donkeys but also half-size rabbits, tiny chickens, pygmy goats and "Chinese water deer," which are around the size of a hefty cat. Only one problem with the deer, say experts. They don't grow antlers at that size. They grow fangs. Fangs? "I don't know why," says Mrs. Culbertson, of the horse association. "God did it, not me."

If down-breeding animals for kicks strikes you as a little decadent, you may prefer to think about the new Mexican "minicow," reported earlier this summer to be smaller than a large mastiff but capable of giving more than a gallon of milk a day. Full-size Brahmans weigh about six times that, and eat accordingly, but produce only half as much milk. Breeders predict a virtual agricultural revolution, especially in the Third World.

Amid all the excitement, we offer only one caution. What if someone down-breeding those little deer with fangs should inadvertently breed them back up, producing full-size fanged bucks? Didn't think of that, did they?