I concluded that mounts were more trouble than they were worth. They would fight and get injured because they had no armor. Or they would get scared, toss the rider, run off, and never return.
Pack animals, OTOH, I found to be extremely useful.
In either situation is it possible to tie up/secure a mount or pack animal before going into a cave/dungeon/tower?
I haven't played much adventure like some other players on these forums. But FWIW, here's my untested theory: You can talk to the animal and tell it to stay put. If you then lead or mount the animal and it later breaks free, then it will return to the last spot where you told it to stay. If you (t)alk to the animal and tell it to follow you, then you wipe out that spot and your location become the animal's destination. But just as with companions, the animal sometimes will not follow you if the distance is too large. But if his instructions are to return to a fixed location, then I think that he will always go back there.
So yes, you can leave your animal behind before entering battle, and it will probably be there when you get back. But that may not be wise. In my limited experience, unmounted animals don't seem to draw aggression, and they are slow to enter combat. Mounted animals OTOH will immediately attack whatever you attack, which generally gets them maimed since they have no shield, no armor, and low fighting skills.