I get a steamy mirror all the time. I don't have a preventative, but my cure is a chamois "doughnut", which I bought at the Container Store. It's a bunch of little chamois squares strung in a circle on a cord. A regular chamois cloth would probably do just as well.
I have tried t-shirts, terry cloth, and fake chamois cloth, but the *only* thing that gets the mirror shaving clean, in a visible sense, is chamois. And it doesn't leave any fluff on the mirror either.
