Horses.

[Scud]

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 ?

Dismounted horses in the old Talonsoft version of CS were fixed, so easy targets. It was widely felt that a horse wrangler would have stayed with the horses and moved them to safer pastures, and bring them back to be mounted again. So Jason and the crew at Matrix implemented that in the first Matrix version of the game.

As for your second question, HA!, I don't think anyone ever thought to test that.   Maybe Jason and the Matrix team will address that in the next update.

Dave