[NightKnight]

It may have survived, sure, but I think it's more likely that it died, and that he got a new horse.
I think he rode the horse from Minas Morgul because it would have been easier to command his army that way. Just ride in the front and, later, send forth the troops. With the big dragon-thingy he would have to land every time he would give a new order, not to mention that the other horses in the army wouldn't have liked it.