She appears varnish Appaloosa, however they doesn't really clarify any specific breed/breeds since Appaloosa patterned horses can be a mixture. That being said, you wouldn't be totally wrong to refer to her as an Appaloosa.
As for horse or pony, that again would depend on her breeding. It used to be said that anything under 14.2 was a pony, however many Quarter Horses and Arabians come under that height and some breeds are no longer being classified as "ponies", though you seldom find them exceeding 14.2hh (Fjords & Icelandics to name a few).
Therefor, i believe it is now more of a personal preference. I call my Fjord a horse and my minis ponies (though they're technically "miniature horses")