Aren't the events themselves divided by gender? (i.e. what your are describing is a result of the way competitions are structured, not a symptom of preference) I don't live in a horse area but have family that ride high school rodeo out west, and I thought rodeo events were divided by gender so that women do barrel racing, and men do roping (for example).
The categories feel less explicitly gendered than "historically" gendered. I've seen many female ropers over the years, though they are definitely outnumbered by men. Of course, most of those competitions were at the extra-cirricular level.
