BURLINGTON — Whatever you do, DON’T call them ponies.

Just because they’re cute, tiny, cuddly and come up to your waist. These are full-blooded horses, thank you. They don’t think they’re any less than the great Secretariat.

“They don’t like to be called a pony,” Debbie Hatcher said. “I tell people that.”

Hatcher ought to know. For the past three years she has been owner and caretaker of Rocky and Thunder, two miniature horses that weigh about a tenth of a full-sized steed and could fit under an office desk.

They call home the back part of Hatcher’s Greenhouse, the three-acre nursery which Debbie and her husband, Jay, have owned and operated since 1994.

Hatcher had seen them at a farm in West Virginia and found them adorable. The next Mother’s Day, a horse trailer pulled up outside the nursery and out came Rocky.

“I was totally shocked,” she said. “What am I going to do with a miniature horse?”

What she did was get another one. Now Rocky and Thunder have a formed a tacit partnership to entertain the clients, especially children, who come to the nursery.

“They need some type of companionship,” Hatcher said. “You don’t want to buy one and leave it by itself. All animals like attention.”

As far as a utilitarian reason for reducing the size of the animal, miniature horses can pull their own weight and more, literally and figuratively.

Because of their size and ease in training they can be used in the same way as seeing eye dogs are. They also can be ridden by a child, who is under 80 pounds, or can be trained to pull a buggy.

What a new owner has to watch out for is feeding. Just like anything of small stature, a little bit of overweight really shows.

“You will see some out in a pasture,” Hatcher said. “Some will get too fat and look like a pot-bellied pig.”

Only a handful of grain or oats each morning and evening and a flake of hay twice a day is what Hatcher feeds her pair.

And to make sure they keep their boyish figures, Hatcher has been known to take one or the other out jogging through the park at the Sybene Senior Center.

One time Jay Hatcher was trying to track down his wife and went up to the park. He asked a man if he had seen a woman and a horse jog by.

“Yeah, right,” the stranger replied.

Then, in minutes over the hill came Hatcher and her horse.

“You weren’t kidding, were you?” the stunned man said.

Wisely he didn’t add, “What a cute pony.”