At 14.2 HH a pony becomes a horse. So from 14.2HH up the equine is considered 'horse'. Some of the biggest horses can reach 19 or 20 HH. That's a pretty big horse.
The Australian Pony, A pony of the mesomorphic type, standing 12-14 hands (1.21-1.42 m) at the withers. temperament: Well-balanced Qualities: Strong, Healthy, Well-suited for young children.
The average size of a horse is about 14.3 to 18 hands high, but it really depends on the breed. Same with a pony, but the largest size of a pony can be 14.2, or else it would be considered a horse.