Steps to reproduce:
1. Mount Horse
2. Log off and Reconnect
3. Dismount horse
4. Punch horse (MC-16156)
The game now thinks you are holding shift, so if you try to get back on the horse, it will only show the inventory. (To fix, press the shift button once, that will unlock it.)
Confirmed.
No need to punch the horse, some other things (don't know which) trigger this issue too.