I read a very interesting article couple days back. You have to sum the temperature (in F) and humidity. Say if temperature is 80F and humidity is 40%, then we are talking about 120.
If the sum is up to 120 - it's OK to ride normal, 120 - 150 - OK to ride but check the horse on any sign to be dehydrated, over 150 - better don't ride.
Of course, it depends on humidity a lot. Say, 100F + 30% humidity is much better then 80F + 50%.