I haven't seen any vids showing people riding mounts in PvP battles. Will there be cavalry?

I personally would not want them in PvP.

You can ride mounts in Cyrodiil. Is there mounted combat? No clue.

I wouldn't mind if you were allowed to ride them in Cyrodiil. That is completely fine with me, just how with the action combat is setup it would be really hard to be a archer and on a horse running at fast speeds and trying to hit someone and vice versa if on the ground trying to defend.