If you are out for multiple days, you need to stay DRY. Yes, dry. This means that you need lots of thin layers; this includes your socks and gloves (think insulated overboots and over mitts). And you need to shed and dawn layers to match your exertion level. Pace your self to avoid significant sweating. Choose your layers carefully so they wick moisture from your body and carry it to the outside. Remember to vent your sleeping bag at night if you find yourself getting too hot.
Your extremities cool down first.
Never lie your mittens or gloves down, instead tuck them into your parka next to your core where they will stay warm. Release buckles on your hard shell boots whenever possible; compression reduces circulation. Wear loose fitting and flexible mukluks as much as possible to help insure good circulation in your feet.
Avoid standing for long periods of time in extreme cold, your hands and feet will cool rapidly without additional insulation or exercise.
Avoid removing boots to check for frostbite when traveling in below freezing conditions; do this ONLY after camp has been set-up. Exposing feet to the cold—even if you are putting them on someone's belly to warm up (Brrrrr)—does not work unless they can go from a warm belly into warm booties, mukluks, or a sleeping bag. If you are traveling and you attempt to warm a friend's feet without a camp set up, where do you put them once they are warm? Back into cold boots that have been cooling further the entire time you are warming your friend's feet? This is a guaranteed recipe for frostbite.
Eat & Drink enough.
Make sure you carry enough calories to meet your energy demands. Use simple carbs to get the internal fire going then load it with protein and fats (logs). When it's extremely cold, consider carry a "food bag" around your neck as you hike (ski, etc.) so you can keep munching when you need it most. Calories in, energy out. Make sure to eat a good dinner with logs and take a carbs/protein/fat food (peanut butter fudge for example) to bed with you to eat if you wake at night. In addition to calories, you'll also need adequate water. Drink it cold if you are hot and hot if you are cold.
Get into your sleeping bag HOT!
This is perhaps the biggest thing to remember to sleeping warm when it's cold out. If you get in your bag and your are NOT hot, you will likely be cold the entire night. Here's why: Your sleeping bag is cold when you get in it; you've got to warm it up and trap heat to sleep warm. If you get in cool, you'll be cold once the sleeping bag "sucks" what little heat you have away. So...go for a hike, ski, etc. until you start to feel too HOT (don't pass the sweat point), then get in your bag. You'll warm the bag up as you cool down (the cool bag should feel good at this point) and you trap enough excess heat to keep you warm. Store your nightly food stash near your head so you can find it when you need it. Finally, wear a hat and if you have cold feet, fill a nalgene bottle with hot water, cover it with a couple of socks, and keep it by your feet. Toasty. Remember to use a piece of plastic bag to act as a washer to get a perfect seal; you definitely don't want the bottle to leak....
There is a myth out there that you should always sleep in your underwear (or naked) in a sleeping bag. This one's REALLY silly. If you are cool or cold, you need more insulation not less. Bring a few extra layers into your bag with you. If you wake up a little cool, eat something, and put them on. Putting the already warm layers on inside your bag will generate a bit of heat and help you to fall asleep easier.
Put good insulation UNDER your bag.
Here's where self-inflating sleeping pads with reflective mylar really shine. The thicker, the better.
Watch out for wind CHILL.
When it's below freezing, protect yourself from the wind. This includes: wind shells, hood with tunnels and fur (both help trap a warm bubble of air near your face), insulated face masks, and goggles. Wind chill is just as deadly at night: surround your tent with snow blocks on the windward side to protect it or, better yet by far, build a snow shelter. If you cook in your shelter, make sure to have excellent ventilation. Carbon monoxide (CO) gas kills.
Insulate your fuel bottles.
Make sure to tape closed cell foam around your fuel bottles and ALWAYS wear at least a thin liner glove when handling. At -30º F (and below) picking up an unprotected fuel bottle guarantees instant frostbite. Be careful not to spill the fuel onto your clothes.
Know the weather forecast.
Read the sky (and your barometer). Keep an eye on the weather and make sure you have the supplies to deal with changing temperatures. Be prepared to turn back if you don't.
Not everyone has the same metabolism.
If you are a trip leader don't judge the temperature of the individuals in your group by how you feel; you are likely to be wrong. A few things to think about: muscle burns fuel all the time, even when "idle," therefore, muscular people are generally warmer than tall, thin people. Men are typically warmer then women. Warmest of all are typically those squat muscular people with a layer of subcutaneous fat (think Inuit), while coldest are the thin adolescent girls/women. Constantly monitor the members in your party for the early signs of hypothermia. If it's extremely cold or there's a breeze, keep a close eye out for the tell-tale white, shiny skin that is the hallmark of frostnip (superficial frostbite).
What if there is an unexpected and steep drop in temperature?
If the temperature drops suddenly during the day, triple up folks at night: Zip two sleeping bags together, put the thin, colder people in their own bag inside the zipped together bags with a warmer person on each side. Use parkas to insulate the outside persons' heads.
If the temperature drops suddenly at night and you wake up. Get up and check each person in your group. If there are any cool people, triple up as above mixing colder people with warmer ones.
Learn to use a pee bottle.
Pee bottles are great...if you don't miss or spill. It takes practice (really)...and some people never quite get the hang of it. Note that it's better to practice in warm weather until you master the skill. It's nice not to have to get out of your sleeping bag and shelter to pee in the middle of the night.
Learning to live and travel safely in the snow, ice, and wind requires practice. Practice implies some degree of failure. If you are teaching winter camping skills, it's prudent to return to a cabin each night for the first few nights of a long course or trip to allow your students the time to master the skills necessary to keep warm.