Ditto ColtysHeart.
One of my horses developed a dry cough after we moved to Middle Tennessee. I started wetting his hay down when he came in at night and it was 95% efficient.
When my 20 yo TWH was diagnosed as being EMS, I had to start locking him up at night, instead of letting him have the run-in stall attached to the 100' X 24' paddock.
I switched him with the dry cough horse. That was one year ago. The dry cough horse (and the others) still get all their hay wet down, but this horse has not coughed once since I got him out the stall.
The EMS horse that is in that stall has never coughed, so evidently Mr. Dry Cougher's lungs were just sensitive enough that being in that stall all night affected his lungs.
My stalls are pipe panels, there is way more than ample ventilation and I clean stalls every day, so it was just something about not being able to move around in the fresh air that bothered him.
So again, I totally agree with the hay wetting and as much turn-out time as he can have
Another last minute thought: There might be something in the hay that he is sensitive to. In general, the 2007 hay certainly wasn't a bumper crop and hasn't been anything to brag about.