Here is a suggestion for your coughing horse - leave one corner of the stable bare to the floor and pile the hay there. If you imagine every time your horse pulls at the hayrack, even soaked hay if it hasn't been eaten within an hour or so, will shed pollen and dust straight down into the horse's nostrils.
Just a thought....I'm sure you've already got a solution for this in place...and really just want to know what it is!!! Hope you don't mind me picking your brains!