Horses.

[Oldbones]

I am playing a game where I have cavalry, that's fine and they are quite mobile.
 I dismount my troops from their horses, but I can still move the horses with nobody on them, I am assuming that they are taken care of by somebody looking after them and they can move them, it that correct ? 
 The odd thing is, I can move them a bit further if I click on save action points for firing, can horses fire even when they are empty, sort of like halftracks ?