Horses a can be in the ā or the ō category, depending on what you do with them. If the horse is a pet, then it is in the ā category. If I had a pet horse, I would say:

tāku hōiho
my horse

But if you ride the horse, then it is a means of transport and so it is in the ō category. If I had a horse I rode I would sayL

tōku hōiho
my hourse