"I have no idea why it works, but if I don't chew gum my throat and lungs burn like crazy and as soon as I warm up again, I cough, and cough... "

I found out the same thing. I always have to cover my mouth when I go out. The gum helps with moisture. Cold air is usually pretty dry, plus you may be mouth breathing which dries you out even faster.

I don't have studs and there is packed snow just about everywhere. This is my first winter trying to ride at least once a week. Last week it never got about 11 degrees. This week we got 10+ inches of snow. I am guessing this will be another no ride week.