I had a few students who just couldn't help breathing through their nose. It just didn't help if I kept telling them to breath through the mouth so I had to try something else:
I tell them to stop playing completely when they need to breath. Then they take a deep breath through the mouth and continue. They will take the habit of breathing through the mouth after a week or two and won't need to think about it anymore. Of course you can't play like this in rehearsals or concerts but you can do it when you play by yourself. Using that method, the few students I had with this problem learned to breath through their mouth in about two weeks without me having to remind them every minute!
I am associate principal horn of the Singapore Symphony Orchestra and the author of the progressive methods. I'm happy to share my experience as a horn player and teacher with you.