First as a GM assume that the mount is always doing the last thing the player said and as such is fair game for messing with. So make the mount make checks not to get spooked and run off in certain situations if it with the group. If the party is attacked by goblins then the horse should be the primary target. If they're going to climb a wall then ask what the player is doing with the mount, if he leaves it tied up to a tree and never says he's going back for it then the next time he says he mounts it you simply say sadly you finally remember you tied it to a tree three months ago and no doubt its well and truely dead by now
If the player leaves it in a village to be cared for while they do a particular adventure then its there until that player goes back to get it or asks someone to go fetch it.
Its a tiny amount of bookeeping on your part, just make it clear that unles advised otherwise the mount is left doing the last thing the player said, you are never going to assume it comes along. if the player can't be assed making it part of his character then your within your GM right to say though neglect you no longer have it. If the player makes the effort to keep it round then he deserves the benefit