First of all , Try and listen to Jimmy's Version of the Song, It's a lot more Ride On, The lyric is run the claw along my gut one last time, not run your claw. What's the difference I hear you ask?

Run the Claw denotes Emotional Pain and Distress that Goes on.
Run your Claw denotes Physical Pain and Distress that ends quickly,

A lot of people seem to think that this a song about a horsey, it's not, it's a song about the pain of living life and life is hard, Ride on.

I'm surprised that people think the song is about a horse

True You Ride the Finest horse I've ever seen....

This sounds like the song is directed to the person on the horse and not about the horse itself.