Your camera will be fine, I've been out in very sub-zero temperatures, to the point where lens hoods were freezing white, and never had a problem. As Ken says your battery life will suffer, carry spares and keep them close to your body till you need them, eg in inside pockets. If you're doing long exposures keep an eye on the front element of your lens for condensation forming.
Again as Ken says you'll get cold before your camera does, a good pair of gloves is a well worthwhile addition, I use Sealskinz Ultragrips and some neoprene fishing gloves with foldback thumb and finger and they keep me out year round.