Thanks for the replies. My general approach has been to practice off turf if possible, even though sometimes that means looking for little patches of grass to place the ball on. I only wondered if there might be some benefit to hitting iron shots off the mat, since I see plenty of people doing it--maybe the idea is that if you can hit them off the mat you should be able to hit them off the fairway.

I have a hybrid 3 iron and some sort of "utility" wood with 21* of loft (no number on it), and I've practiced with these off the mat and off the chewed-up turf, but it doesn't matter; I've yet to manage a shot with either one. With irons at least I occasionally connect--maybe 10% of the time. If I didn't I guess I would've given the game up by now.