Lots of excellent points made here; this one's a keeper for winter newbies (and for you infrequent winter overnighters.)
I would add:
1. There's a bigger difference between -20F and -40F/C than a mere twenty degrees. At the former temperature, you're working to stay comfortable and get some sleep. But at the latter, Mother N. is trying hard to take your digits, your limbs, and even your life's breath. If you're likely to encounter the hardcore stuff, you will want to have tested your gear and your methods in some serious subzero conditions before your first attempt at this level.
2. Moisture on your skin is your heat-robbing enemy. Warm, dry sleeping clothes, from a balaclava, etc., down to your sleeping booties/socks, are a must. Don't wear them during the day ('cept maybe the balaclava, if you can get it dry before bedtime.) If you need to pile on the daytime fleece for sleeping, shake off all the moisture, liquid and frozen, before retiring for the evening.
3. Stay well hydrated. Moisture under your skin is essential to keep the furnace running efficiently.
4. Bring some hot water in Nalgene bottles to bed. Well-contained hot moisture will help you get through the night, and you'll have liquid water ready in the morning (usually .....
)
5. A well-ventilated tent is essential if you're going to be out for more than a night or two. Accumulated frost will soak your bag and your clothes.