General terms:
* Pony: This is the most common term for a small horse, but it's not always precise as some ponies are larger than some horses.
* Miniature horse: This refers specifically to a breed of horse that is under 34 inches tall at the withers.
* Small horse: This is a straightforward and neutral term.
More specific terms:
* Shetland pony: A breed of pony known for being very small.
* Welsh pony: Another small breed of pony, known for their strength and athleticism.
* Arabian horse: While some Arabians are larger, they are generally considered a small breed compared to draft horses.
* Thoroughbred: Though not typically considered a small breed, some Thoroughbreds are smaller than others.
The best word to use depends on the specific context. For example, if you're talking about a horse that is less than 14.2 hands tall, you might call it a "pony." But if you're talking about a horse that is specifically under 34 inches tall, you would call it a "miniature horse."