Ride a horse with a saddle like you would normally do and log out. when you come back in the horse will be paralized. he will be back to normal when you log out and log in again. on multiplayer the horse is duplicated.
Linked issues
duplicates
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Since you closed this i will make another issue with all fields complete
Since this has been reopened, I too have seen the paralysis issue as described by OP. I have not yet tested the multiplayer component of their report though.

Duplicate of MC-16182
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