You con not tp a horse to a location when you sit on it:
sit on a horse and type:
tp @e[type=horse,r=10] ~ ~10 ~
It will not work
tp @e[type=horse,r=10] @e[type=pig,c=1]
will work

ps: levitation willl also not work when you sit on a horse... the same problem i found by boats and minecarts