The horse belongs to the Family Equidae.
Some basic background: The horse belongs to the Family Equidae and the Order Perissodactyls. The first fossils found belong to the Cenozoic Era approximately sixty million years ago. Back then it was two feet long and fourteen inches tall weighing and averaged fifty pounds. Today we define a pony as a horse which is less than 14.2 hands tall and a horse is taller than 14.2 hands. (A hand is equal to four inches and a horse is measured at the withers.) There are no other differences between them anatomically speaking.