Sorry to be pedantic about terminology, but there is only one species of domesticated horse: Equus Caballus to which all horse and pony breeds belong. 'Pony' is just a term used for certain breeds of horse, and is to do with the relative proportions of leg and back length and general shape. The tiny Falabella for instance is a miniature horse, not a pony. All ponies are horses, not all horses are ponies. Falabella, Arabian, Throughbred, Akhal Teke etc are all just breeds of the same species, just as the wide variety of domestic dogs are just breeds of the single species Canis Familiaris.
Phil Sidnell