Warmount is equipment?

Exotic War Animal ability speaks of mounts as equipment. I've gathered that Warmount ability makes the mounts equipment. And with the Mount ability you can dedicate an entire class to being a Mount and you can add Traits so you don't need Exotic War Animal ability. I've also assumed that this means a model from another class can just sit on the class with the Mount ability (it is not equiped as a Warmount). But now that I've reread the rules it does not say this explicitly. Are my thoughts correct? And if not, could you point out relevant texts please? Thank you in advance.