Paladins used to get a spell at lvl 20 I believe, but haven't played that class in quite some time. Very slow horse though, compared to the rest.
There are a couple of mounts that are pretty much lvl restricted: the carpet and the wargs. Rinoceros most definitely is too, as that also requires quests to be done before you can talk to the vendor.(wargs and carpets have specific quests before you get one or can buy one)