Personally, I think this looks fun

Archery. Horses. Competition. Those three words ma' dear can strike excitement into this girl's heart at the drop of a hat. As of yesterday, I found that my very County has a group of medieval reenactors, and for no cost at all, you can join their group and learn all sorts of fun stuff like broadsword fighting, rapier fighting, jousting, and of course equestrian events like mounted archery. *Swoon, faint* 

I didn't think much else could top barrel racing when it came to exciting horse events, but this mounted archery looks awesome! This video shows the basic level of the sport. Higher levels include jumps to go over, water to cross, and other cross country events.

"Teddy, I need a horse."