80F is absolutely no problem, it's really not even that hot. Like you said, most of the show season will be done at that temperature and they don't go out and cancel the show just because it's hot.
At our barn, we'll cancel lessons if it gets past 95F, but I live in a very humid place so it gets a bit harder on the horses than if it was a dry heat. We never cancel the summer camps though because the horses are simply walking around for 30 minutes/day.
Maybe just have lighter rides on those days, and more importantly, just listen to your horse. If they feel fine and are breathing fine, I see no problem riding them.