Hi There,
There are 2 main issues:
1. Condensation - Its typically much colder and dryer outdoors in winter. When you bring the camera indoors, there will be condensation on all the surfaces, and it will be more severe than what we experience here when we take our camera from a cold air-conditioned indoor enviroment to the outdoors. The safest way to deal with this is to put the camera and lenses etc back in the bag before going indoors, and then leave it in the bag for a few hours before taking any of them out again.
I'm not sure about the Ziploc and straw method which the other poster mentioned. I've never tried it, but I think a lot also depends on the temperature difference between indoors and outdoors. The greater the difference, the heavier the condensation, and the longer I would leave it in the bag after I take it indoors.
2. Battery life - Batteries conk out faster in the cold. As others have suggested, bring spares if you are going to be out shooting for a while. Keep the unused batteries close to the body to keep them warm so that they will last that little bit longer. Remember to re-charge them in sufficient time for the next round of use.
Apart from these 2, I haven't really encountered any other problems. I would only add that if you are photographing outdoors in snow, do check if you need exposure compensation.
Hope this helps.