The question is also on Dr. Robert Beard (Alpha Agora)
wherein it was originally posted, and a person there
asked me. Here is Dr. Beard (Dr. Goodward)'s response:

I must admit this is a new one to me, too, so I can only surmise.

I would guess that since the fetlock protrudes from a horse's leg, grabbing life by the fetlock would be to lock onto it in a way that it cannot escape. In fact, horses that were hobbled were usually bound by a "fetterlock" to the fetlock.

The "lock" of a fetterlock and that of a fetlock are not the same. Fetlock is a reduction of foot + lock in the sense of a lock of hair.
_________________
•The Good Dr. Goodword

----please, draw me a sheep----