Re: Why horses?
Since it's fiction, you could come up with any reason for the superiority of horses as mounts in a given campaign. Probably the simplest is trainability--in real life, zebras simply cannot be tamed, even though they seem to be the same animal except for the paint. Elephants can be tamed, but not to the degree that horses can; even the most carefully trained elephant was easily spooked in battle, and modern working elephants go berserk on occasion. Semi-tamable predators like bears and big cats can't be kept in large groups lest they kill each other.
Conversely, in fantasy it's pretty easy to handwave all this stuff away and make wyverns or wolves or tauntauns or dragons or armored polar bears the superior mount.