This might not be terribly helpful, but I think this is one of those situations where you can take the spectrum of normal human behavior and use whatever fits your story.
I've been involved in a couple of school 'equestrian teams' but both were atypical (both at same-sex schools, and neither intercollegiate or particularly competitive) and I was always more a keeping-to-myself sort of person. So if events happened I only ever went because I felt I had to in order to continue getting discounted riding lessons. But anyway...there were certain functions, the usual thing you could expect...fundraising, dinners sometimes, throwing crap together and bathing the horses before a show. Most of which, as I said, I ducked out on, so I'm no help at all. But where people are in contact, they might come to like each other. Or hate each other. Or neither. Whatever. You can do what you want with it.
I don't know that people would be hitting on other people *at* shows, though. Maybe, but the show drama, in my experience, is more about bitching about other people's crap riding and crap saddles and what did they do to their horse's mane and I heard she was friends with that girl who wears capes and oh my god is that GLITTER? And when not doing that, things can get pretty busy with memorizing your course and knowing your number order and hosing off the horses and tacking them up and switching and hot-walking them and changing and blah blah blah.
Anyway, in short: it's a group of young people getting thrown together in situations where drama can potentially happen. That's pretty much it, socializing-wise. You can manipulate it pretty freely, I should think.
