It appears you can gain stealth skill while on a horse. This seems counter intuitive, so just thought I'd mention it. You get revealed if you try to move on the horse while "stealthed", but I figured you would get some kind of error message if you even try to activate stealth while on a horse.
I think this is the correct behavior of it -- the check against the mount movement, I believe, only occurs when you move.. the use check is purely the check against hidden status/skill, then the attempt. I could be wrong, but thats how I always assumed the mechanic.