The camera should operate fine, the issue you will have is the battery will freeze. It will show as being empty, but its not. So having a second battery tucked in to your jacket, close to your body to keep warm, is a must.
When battery 1 freezes, switch for battery 2 putting battery 1 in the jacket to warm up.
The one issue to watch out for is when you come back inside with your camera and the condensation that can form when you are going from cold to hot. Do not turn on your camera right away when you are in doors... condensation + electronics aren't the best match.
Wait a few hours. I usually leave the camera in the camera bag for 2 hours, in my house entry way (which is a wee bit colder than in the house) to let the camera warm up slowly. Some people put the camera in a zip lock bag right away, close it, and wait 2 hours.
Others carry those little salt packs that you get when you buy a bag in the bag as they absorb moisture.
But other than that, you are fine to actually shoot in the cold.
I took some pictures in January 2009 at -25C outside (without windchill) and had no issues (not even with my battery?!?) with my XSI.