Yeah same, It kinda sucks because I stopped bothering to tame horses in my playthroughs.
Also, if you want to tuck in for the night, the horse will deny you any sleep because right now the game doesn't register a tamed animal as 'NOT dangerous'.
Hopefully in future updates there will be a difference in wild and tamed animals, and maybe some commands were you can tell the horse to wait and/or follow you from a certain distance (close, medium, far).