Its a sad statement that Michelle's mind could go "there" first when this joke is told vs. the Farmers perspective of an idiot getting their butt kicked by an angry animal. Which is where the mind used to go when this joke was told.
The only appendage that hangs from the bottom of a male horse that even remotely resembles a cow's teat, is a penis. This is exactly where this joke always went, and I heard it over 50 years ago. As soon as Laura said it was a male horse the joke was about masturbating the horse, it had nothing to do with trying to milk a mare.