Obviously there are some specific hazards unique to winter camping, including hypothermia, frostbite, and avalanches. But really -- and I realize this is stating the obvious -- what sets winter camping apart from your three-season jaunts is the cold. Cold complicates everything. It interferes with movement, agility, breathing, eating, drinking, you name it, the cold is in the way. Hopefully it's never more than an inconvenience, and a minor one at that.
Things get ugly in one of two ways: a situation that exceeds your limits, or a situation that you've screwed up. A situation that exceeds your limits might include being trapped under the ice in a lake. A situation that you've screwed up might include walking out on the ice in the first place without taking some precautions -- carrying a long pole horizontal to the ground, for instance -- to stop a trip through the ice.
So two questions to ask yourself before you go out -- and throughout your trip -- are: what are my limits? and: what might I screw up? Then do what you can to protect yourself in those situations.
You need to know enough about what you're doing to answer honestly. Much like in a court of law, ignorance is no excuse... or as a sign I read in Estes Park says: The Mountains Don't Care.
Some hazards only become apparent with experience. I, for one, shudder when I think of my first solo winter camp: PVC rainsuit, three-season bag and tent, and I'm sure plenty of cotton. I froze my ass off, barely got my food heated, and packed up as fast as I could the next morning (don't ask me why I ever decided to do it again; I couldn't tell you).
HYPOTHERMIA
Also known as freezing to death, or dying of exposure. This is public enemy number one for our purposes. Hypothermia wipes people out when it's fifty degrees out, so needless to say it can easily take you down at ten below. Personally, I worry most when it's above twenty-five degrees or so: things get wet, which speeds the process of becoming hypothermic.