Living in Florida is quite different from living in Arizona but I believe the heat index would be treated much the same.
I’ve always been taught to calculate the heat index (for riding/working) horses in the following manner: temperature + humidity – wind speed = heat index).
When the total of those 3 numbers is:
~less than 100, OK to do moderate work.
~between 100 and 120 you are OK to do light work.
~above 120 ONLY ride with extreme caution and make sure horse stays hydrated…also rinse off with cool water as often as possible.
If you have ANY doubt it is safe to ride/work your horse it probably is not.