To ride or not to ride?

Since you're indoors out of the sun, there's a bit of a breeze from the fans, and you're just walking, you're certainly OK to ride. There's A LOT you can do at the walk: walk/halt/back transitions, turns on the forehand, leg-yielding, riding bareback and bridle-less to get him to respond to just your legs, weight, and voice cues, desensitization exercises (ride him across a tarp, for instance), different speeds at the walk, etc. Go for it!

It's perfectly fine to ride as long as you keep it low key. Walking and even trotting would be fine. Just make sure your horse is properly hydrated and if he/she looks like they're wearing out then cool them down and cut the ride short. I go on low key trail rides on days like that and I just make sure there aren't tons of hills and we can keep in the shade.

If you want to ride, go ride. As long as you keep your horse hydrated and don't push him too hard, you dont have to just walk. But its perfectly ok to go riding :) I want to but i got to clean...so yea im kinda jealous of you :p