It is important to have a relaxed and fluid air flow while you play. I had the chance to have a few lessons with Mr. Vincent Chicowitz (former principal trumpet of the Chicago symphony) who taught me to practice just the air movement without any instrument or mouthpiece. Basically, you just practice your music blowing the rhythm as you would blow in your instrument if you were playing normally. Groups of slurred notes are blown like one long note like a tie over. You practice a difficult passage like this two or three times and then you go back to your instrument. It feels great! It really helps for passages in the high register. I personally do it every time I feel my air is a bit stiff.
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.