The horse can't "disappear" permanently, just like your companions can't. If you somehow lose track of your horse, you simply need to fast travel somewhere, and the horse will show up there, too.
If you fast travel inside a city, the horse will usually be teleported to a stable outside the city or to some other location around there if the city doesn't have one.
However, horses in this game are particularly proud (they're nord horses after all), so what might happen is that your horse runs away, gets attacked by something and tries to defend itself, dying in the process. Sadly, the "fast travel" trick won't work if the horse is dead.
There is also a random stray horse, free to take without stealing in between Valtheim Towers and Ivarstead