Instead of covering your head to warm the air you breath, you may want to try the ear loop face mask found in drug store at night. I have found, by accident, that it can help if your airway or nasal passages are irritated and cannot tolerate the dryer cold air.

Once when I had a cold, I slept with one to contain my germs. Didn't want John to catch what I had. Found it kept the air moist and warm so I could fall asleep quicker.

They are the probably the lightest masks on the market so have better oxygenation than you would putting your head under the covers. You're not rebreathing what you exhaled nearly as much. But you have to change them pretty often because they will harbor germs over time.