What are you treating it with?
My guy has seasonal heaves as well, this week he is really bad so he is back on his vet meds, Dex and Ventipulmin, and I would not ride him, he is wheezy but not coughing.
When he is breathing normally again I will start to ride him, exercise is good for him, but he will be going out on the trail, he can't be in an inside arena, and even the dust of an outdoor will affect him.
Each horse is different, I would definitely look at some herbal supplements, my vet actually encourages their use, together with good management practices to maintain my guy, it is usually just this time of year that he needs the meds.
It is frustrating, and it is trial and error, if he is having a bad day, just quit, don't push him, if he is doing better then enjoy him.
“Never attribute to malice that which can be attributed to stupidity”