How to stay cool while riding horses in the summer?

I live in fairly hot California weather, and I ride at my local equestrian center. I recently bought a new helmet, an IRH helmet that has 12 air vents, and I ride in thin riding tights and light weight t-shirts. I ride eventing style, so I am jumping a lot, and working on dressage. I am in good shape but I get so hot! My face turns bright red, my helmet turns into a furnace and I sweat like crazy! I have thought about trying some sort of cooling headband or something! I ride sometimes three horses each day, and I would like your help!