Miniture Ponies are great for little kids as they are obviously small, and very well natured. Miniture Ponies range in sizes sepending on how tall their mothers were/are. Some range from 10HH (hands high) to about 15HH.
They're actually called miniature horses. I own some. Mini horses actually look like tiny horses, like little Thoroughbreds. They're really lean with thin legs and elegant heads.
Ponies are stocky...