They do have issues with dust, pollen, etc. My mare was allergy tested and could have no rye, had to watch for molds. She was fine in winter, spring was hard with pollens, etc. I used some Albuterol when needed.
Run-in instead of stalled, careful with beddings (dust)....mats and limited pellets helped. Wet beet pulp helped with the hay issues but, she could eat grass hays if not dusty....wet the hays. Mine mare also lost weight, they seem to get anorexic, but not all the time. Mostly she was in fine health and weight. She never dropped off in foaling/nursing. Fed her less and more often. I have three lovely foals from my mare, she producted 8 total and 7 were colts
: I kept the only filly -- checked it several times to be sure as I just knew it was a miracle -- and 2 colts. So far, none of them have any heaves issues and are 5-9 yrs old. It is an issue that can be managed, most times.