So, my GM and I disagree on a key aspect of riding an undead horse. He thinks that because riding a living horse is about as tiring as jogging, it should be the same on the undead horse. I agree that riding a living horse is tiring, but the work the jockey has to put into riding the living horse is a) to keep from tiring the horse out prematurely and b) to prevent the rider's weight injuring the horse, neither of which should apply to the abomination against nature my character is riding.
Oddly enough, I believe the rules are already in my favor, because normal riding doesn't appear to take actions and therefore shouldn't be tiring at all, allowing me to go on only obeying the rules for the need for sleep; but it's very rare I do anything with mounts in my own games and I'm pretty rusty.
(Because I can be a bit of a rules-lawyer, here are some specific things this question is not about: Rule Zero, whether a fast zombie can be a corpse companion, whether an undead horse can count as "war-trained".)