I do, but I resist diagnosis. I don't like taking medication for what I perceive as a variation of normal... But do take your pump with you!
My airways do not really swell, but they get filled up with snotty goop. Thus the snot rockets (which, I know, you abhor) and some degree of spitting.
I find it a lot easier this year than last year, too. I think it becomes a habit. It's always easier to do it progressively. I'm glad I started running consistently in September, so I got used to the change in temperature... Perhaps you could try going for very short periods at first, like 10-15 minutes, and increasing your times progressively?