If it is a musty/moldy dust then I would agree about not using the hay. But, if it is a dry dust as AJ describes then it is pointless to burn/dispose of the hay, because any other hay you get in this area this year will be the same.
The hay we have here this year is very good quality, but it was baled dry and there is a certain amount of dry dust in it--the grass bales are not as dusty as the alfalfa, and the reason the alfalfa gets this dry dust is the leaves are so dry that they crumble during the baling process. The drier the leaves the more they crumble, and crumbled leaves = powdered leaves = dust.
The dry dust won't affect horses the same way that the musty/moldy dust does--a horse with dust allergies or actual heaves will have problems, the others generally won't.
If you're feeding small squares it is easy to shake out the flakes as you feed them--that is what I always do with mine, and any dust that is in them will come out. Again--talking dry dust here, not the musty sort of dust that billows out like a cloud of smoke when you shake the hay out. That dust that puffs out like a cloud of smoke is not healthy and hay with that sort of dust should not be fed. When you're feed the big squares or the rounds, shaking the hay out isn't really an option--not if you've got the bales set out for the horses. Obviously if you are forking the hay out to them, then it can be shook out just like the small bales