Try to fit in the horses that need the most work at the cooler times of the day. That way you'll be able to focus better and be more comfortable.
Riding in shorts really isn't that bad. I mean, you don't look professional but who cares when it's so hot right? But if you can't ride in shorts at your barn then where your shorts when working and then change into breeches when you go to ride. Don't where jeans! They are wayyy to hot most of the time!
Remember to keep water with you!!