When dressing for very cold weather, think layers. Many layers of thin clothing is much better against the cold than few thick garments. The reason is as you have probably guessed, the layers of clothing trap air between them that serves as insulation. If you dress properly, it is amazing how little clothing will keep you warm even in the most extreme cold.
Avoid tight clothing when dressing for the cold, loose fitting garments are much more effective in creating the insulation you want. Typically, a short sleeve undershirt, long thermal underwear, a light long sleeve sweater, a baggy pair of jeans and a windproof loose fitting jacket will keep you nice and warm in most conditions. If you are going to be active, even less clothing is required. Keep in mind though that you should always cover your head, and wear gloves or mittens. A massive amount of body heat is lost from the top of the head, and something as simple as making sure you wear a hat will make it a lot easier to stay warm.
For the best protection against cold weather, the innermost layer should be made of soft spun wool. Not only does wool fabrics have a lot of air pockets, but wool also has the very beneficial property of absorbing a lot of water before it feels wet. In extreme cold,water is your worst enemy, and having a wool layer absorb the humidity around your body will make a huge difference.
Many people like to cover the lower part of their face with a scarf in the cold. This might give some relief in moderately cold weather, but in extreme cold you should be careful about covering you moth and nose. The moisture in your breath will be trapped in the scarf, and over time the humidity could lead to serious frost bite in the face. It is always better to cover your face with a fat based ointment, such as Vaseline, which will protect exposed skin against cold air.
There's an old saying stating that as long as long as your feet stay warm, the rest of your body will stay warm. Making sure you have proper shoes is very important, but just as important is wearing the right socks. It is far better to wear just a thin pair of socks and leave ample room around your foot inside your shoes, than to cram a heavy pair or even two pair of socks into your boots. If you stuff your boots, there will be very little room for air around your foot, and you will get very cold. Walking in the snow with shoes that are too small or that are filled with too many pairs of socks will feel like your walking barefoot. Without insulating air between your boot and your foot, the boots will actually draw heat out of your body as they themselves are cooled down by the snow.
These tips will keep you warm in most normal winter weather for most outdoor activities