After a few minutes of research, I discovered that mud wrestling is not an actual sport. It appears to be primarily limited to fraternities, bars, hillbillies, backyards, outdoor rock concerts, and fishing trips went bad news stories. However, I have not been able to find any sort of regulated, organized, or association tournaments.
After analyzing a recording of a traditional wrestling match, my research found that the vast majority of women participating were scantily clad and their audiences were predominately male. Almost sounds like science has been done on the mud wrestling front.
Unlike the first entry, this second one was much vaguer and not useful in any way. It takes a lot of time and effort to write blog posts with even a little bit of structure.
The New York Times ran an article on mud wrestling which, to my disgust, was about political mud-slinging, not bent arm bars or cross-collar chokes in mud pits.