I was testing around looking for bugs, when I found this little one. If you are 5½ - 6½ blocks away from a horse and you right-click, instead of hopping on the horse, your character's direction will turn a different way, looking away from the horse and not actually going on it. Here is an example...
The first picture of me is 5½ to 6½ blocks away from the horse. The second picture shows my player's angle after I right-clicked.