Interesting visual. This malaphor was seen on Golf.com. It is a mix of “throw one’s hat in the ring” (indicate one is going to be a candidate) and I think “no horse in this race” (not invested or affected in the outcome of something). This is a true incongruent conflation, as the idioms have opposite meanings. “Workhorse” (a person who works tirelessly) may also have been in the mix as the writer was talking about professional golfers who are true workhorses. The writer may also have been thinking of horses in a circus going around a ring. A shout out to Larry Mason who spotted this one and sent it in.