Horse developed sneezing

I moved my horse to a new barn and the next day I noticed he started sneezing. It happens most of the time when I am bringing him in from the paddock and lasts while he is in the barn and for a short time while riding. He is up to date on all vaccines/deworming. I have noticed a small amount of white, but mostly clear, nasal discharge. No other symptoms. What could this be and what can I do to alleviate the sneezing?
He is a 4 year old TB, if it matters.

My horse started doing that out in pasture. It seems that there is something growing right now that is bothering her. I had her scoped just to make sure and nothing else was wrong.