Heaves tends to be progressive, though it may be slowed by controlling exposure to irritants and treating attacks as soon as the first signs are seen.
Stall/barn keeping causes exposure to high numbers of irritants--molds, dust, fungal spores, etc--so pasturing all year is recommended if the horse's attacks coincide with being in a barn. (There are some horses that have "summer pasture associated heaves" which have attacks from plants in the pastures.) Hay soaking, actually serving it in water, during the winter months is recommended as hay harbors lots of irritants and these become airborne while your horse's nose is stuck right in the hay. Soaking and then serving hay out of water will decrease the amount of airborn irritants only for a short while because hay starts drying out in minutes and irritants become airborne again. A single exposure to irritants affects the body for 3 days, so minimizing exposure is critical.
Treatment for heaves is a combination of steroids and bronchiodilators that are administered at the onset of signs of an attack. Depending on the severity of the disease in a particular patient, a vet may opt to only use one or the other of these types of drugs to treat, but in severe cases both are recommended to treat both halves of the disease process. It is believed that giving antihistamines may help to reduce the risk of attacks by helping to lower the body's reaction to irritants. But antihistamines are not an appropriate treatment for an attack.