Sometimes when I get off my horse he turns invisible and leaving the game and going back in brings him back (I can still hear his noises so thats why I said invisible.) This happened on a flat desert area so it wasn't really a complicated surface or area. My horse also went up a couple blocks to another tree branch when I got off him on a jungle tree once. One time I fell into a ravine, got off him, couldn't find him anywhere and when I built myself to the top of the ravine he was standing a few blocks next to it.

Edit: Just got off my horse in a jungle and had to leave the game and when I came back he was completely gone! Goodbye diamond armor.