Having three boys in Boy Scouts, we do a lot of camping, but it's always been in the spring, summer and fall. A couple weeks ago we went to a week-long winter camp, where the temperatures at night dropped down into the 20s. It took a little extra planning, but we all slept warmly, so I thought I'd pass on a few pointers.
Of course, this doesn't just apply to camping trips. In a SHTF situation you may find yourself without power and proper shelter for a period of time, where the ability to keep warm means more than just a pleasant night's sleep.
Let's start with your tent. There are two main styles of tents - three-season and four-season. A three-season tent will have large mesh panels to allow ventilation on those hot summer nights, while a four-season tent will have much less mesh (to retain the heat), and will have stronger poles to stand up to snow and wind. If you can't get a four-season tent, then you at least want to make sure that your tent comes with a full rainfly (one that reaches all the way to the ground). This way the wind will hit the rainfly and not your inner tent wall; you'll have a small space of still air that will give you a little insulation. Also, the smaller your tent, the better - your body can heat up a smaller space faster. Don't go too small though, you don't want to find yourself sleeping up against any of the walls.
When selecting a site for your tent, obviously you want to stay out of the wind as much as possible, but you also want to avoid valleys and sites near lakes or ponds - places where cold air can settle.
Next, let's move inside the tent. You need something that will insulate you from the ground - laying straight on the cold ground will suck the heat right out your body. At the very least you'll want a closed cell foam pad to insulate you; the thicker the better. A step up from that is a self-inflating foam mattress - the foam traps a layer of air inside which retains the heat from your body. We use these Kelty sleeping pads - they have the foam insulation inside, plus you pump them up (using a built-in pump) so that they're about as thick as a pool air mattress. That way you've got both insulation and comfort.
On to your sleeping bag. A mummy style bag is better than rectangular - you want to be able to close off the opening at the end and keep the warm air trapped inside. And don't believe the rating that you see on the package - you can usually add 10 or 20 degrees to the number to get the real rating. In other words, a bag rated for 30 degrees is (for most people) really only comfortable down into the mid-40s.
A sleeping bag works via it's loft - the way it puffs up and traps air inside. Because of this, you should never store your bag compressed for long periods - leave it loosely packed inside a pillowcase until you're ready to travel. And when you get to camp, Be sure to take it out of the bag, shake it out, and give it at least an hour to "puff" back up.
You might be tempted to throw a big heavy blanket on top of your sleeping bag for extra warmth, but most of the time this will actually have the opposite effect. Remember that the bag keeps you warm by being puffed up - if you throw a blanket on top you're compressing it back down and losing some of the insulation. If you need a little something extra you're better off placing a smaller blanket inside the bag.
When you're inside your bag, keep the hood up over your head, but don't keep it all the way over your nose and mouth. As you breathe you exhale moist air; you don't want that to collect inside your bag and chill you. Also, make sure the foot of your bag isn't touching the wall of the tent - that will rob heat from it the same way sleeping directly on the ground chills you.
Now that you've got your sleeping quarters set up, let's talk about what to wear. In most cases, less is better - if you've got a good bag (and a liner/blanket if needed), then you can probably get by with just a comfortable pair of sweat pants and shirt. If you need a bit more, then put a pair of long underwear on as well. You'll want a good pair of thick socks as well. Whatever you sleep in, it should be clean and dry - don't go to sleep wearing the clothes you've worn all day. Finally, be sure to have a hat, and maybe even a thin pair of gloves as well (thin cotton gardening gloves are better for sleeping than your big heavy ski gloves).
Finally, there are a couple things you can do to warm up your tent and sleeping bag before climbing in. A water bottle filled with hot (not boiling) water will warm up your sleeping bag, and stay warm for some time. Be sure the lid is tightly sealed; we like to use Nalgene bottles and have never had a problem with them leaking. If you don't want to use a water bottle, a couple disposable hand warmers will stay warm for most of the night. You can also put them inside your socks if your feet get cold.
If you have the room in the foot of your bag, stuff tomorrow's clothes down there. Not only will they provide you with a little more insulation, they won't be freezing cold when you put them on in the morning.
If you have a place in your tent for it, a candle lantern can raise the air temperature by 5 or 10 degrees. Just be sure it's in a safe spot where it won't get kicked, and the flame is totally enclosed.
When you're ready to go to bed, don't go to bed cold. Do a little bit of exercise first - not enough to sweat, but just enough to get your blood pumping. Maybe a brisk walk, or a few jumping jacks. It's easier for your body to stay warm when you stop moving if you're already a bit warmed up.
Finally, be sure to stay hydrated on winter camping trips. It's easy to wind up not drinking as much in the cold weather, but your body still needs fluids. You can also have a cup of something warm right before going to bed, but not too much - you want to avoid any late-night trips into the bushes.
You might want to try a test-run at home to determine how warm your gear will keep you in cold weather. You might feel a little silly setting up camp in the backyard like you did when you were a child, but wouldn't you rather find out that you need a new sleeping bag when you're 10 steps away from your back door, rather than in the wilderness?
Following these simple steps should keep you nice and toasty at night when the temperatures drops down into those single digits.