Somebody's Horse by Dorothy Nafus Morrison

Jenny Alexander has her heart set on taking jumping lessons on a beautiful horse named Cinnabar. But when her parents take an unexpected business trip, she is shipped off to her cousin in Wyoming instead.

There Jenny begins to take care of a sick and neglected horse that was abandoned at her cousin's home. Newly named Farfalla, the horse turns out to be much younger than originally thought - and well trained.

But the horse's origins remain a mystery, and Jenny begins to think of him as her own. But the questions remain: Whose horse is he? Why would anyone abandon him? And how could Jenny ever bear to give him up?