Good advice above. The most important one is that you don't bring a very cold camera into a warm/humid environment without some protection. For example, if you are outside and it's well below freezing the camera & gear will get cold. If you then go into a building or warm vehicle, humidity in the air will condense on the cold gear (inside and out). So to keep your gear from getting wet, you need to protect it from the warm air until it has a chance to warm up. The best way is to use an airtight bag like a zip lock. At the very least, keep the gear zipped up in a camera bag and let it warm up gradually before you open it.
Also, be aware that cold temps will kill the battery really fast. The best way to deal with this is to have two or three batteries and keep the spares close to your body, inside your coat. When the one in the camera dies, switch it out with a warm one. The cold one should regain it's life when it's warmed up.