Horse in the Nether is invisible for an amount of time (you can hear snorting, though). Sometimes it appears again after a few seconds, other times not at all or only when you left the chunk and return. 

Other times when the horse can be seen it misses its armor and may duplicate when you ride it. The duplication happens like this: You take the armorless horse and leave the chunk the same horse may have spawned (with armor) onto your return to the chunk. The horse without armor usually disappears after leaving the Nether.