The cold weather and the dry air has made my skin very rough. What to do to reverse the effects?

Dry air does suck... ...The moisture out of your skin. After you bathe or shower, apply a good emollient lotion (any brand will do) to your skin while it is still moist, to lock in the moisture. If that doesn't solve the problem, there is more going on than just dry skin, and you will have to see a dermatologist.