I've always used the compressed air method, and it works fine if you take your time, and is easier to dewinterize come spring. That said, both methods are perfectly effective if done properly.
The idea that compressed air is only valid for moderately freezing temperatures is absolute foolishness. Water freezes when it's below freezing, and it doesn't freeze "more" because it's far below freezing. Either the plumbing is (basically) free of water or its not; if it is, you're good for any temperature, and if it's not, you should avoid conditions where it would freeze and burst fittings, etc.