Aha, they might be able to live off them, but would it keep them healthy enough to carry your load of supplies (You need to carry around much more than Cowboys did, don't forget) and be able to outmaneuver a horde of zombies at the same time?
A horse might well work as an individual transport, but you can't regularly count on it to perform well enough in any condition.
Besides that, the point about weapons. If you're being faces by little enough zombies to slip through the gaps with your horse, you can well take them out (At least a fair number of them) with well-placed shots from a battle rifle or similar weapon; it is certainly much safer than trying to run through and hoping the odd zombie doesn't land a hit on your horse.
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