Getting your mounted animal to fight with you is not easy. The mount must first be willing to fight your opponent, and secondly, the mount must think it can win, a first level donkey won't attack a dragon. If your mount feels from battle, there is a great chance that it will throw you off it's back, if you flee a battle, the mount will come with you.
Mounts can be purchased at most trading posts, and many cities contain well stocked stables to purchase. Many animals in the wild can be trained to be good mounts, even though there may be quite a fight at first. Mountable animals are very expensive, and only the richest of travellers can own them. Trading rare creatures as mounts can bring a large income for adventurers.