The quality of your hay and a lot of dust in general can have a negative effect on your horse.
In my stable we have a horse who starts coughing excessively if we feed him dusty hay. Dust will generally have an effect on the respiratory organs of your horse, especially if it is exposed over a longer time. Article on Dust Management and respiratory diseases
If you can, you should not buy dusty hay (duh).
But if you already bought it and don't want to waste it there are still things you can do.
- In our stable the horses prone to coughing get their hay wet. So we soak it in water a few minutes before feeding to make it less dusty. (The article states that merely dipping it in water can already improve the dustiness.)
- Feeding outside (if possible) can help since the dust will spread more and be less focused on just one place.
- The article above mentions to spread the hay out on the stable floor to lessen the concentration of dust particles in one place.
- One more thing from the article is to generally keep the barn open at places if possible to allow for air circulation and reduce the amount of dust.
- Another alternative is of course to not feed hay but this might not always be an option.