If you are using flash, use a cord and get the flash at least a few feet away from the camera. Another concern during snowfall, is the effect of moisture on the camera and lens. Since we are trying to keep them warm, the snow will melt on the camera. You can use commercially available waterproof devices, or you can simply grab a plastic bag and drape over the camera and lens. Make sure you have a lens cleaning kit available to clean the droplets off.
Condensation is yet another problem.
Taking the same cold camera from the outdoors back inside will however, cause condensation to form. The best way to deal with this is to put your camera into your camera bag and cover with a towel or coat as soon as you get indoors. This way the camera will warm up slowly and moisture will not form on to it and potentially cause problems. Some sources suggest that simply putting the cold camera into a sealed plastic bag while outside, and then taking it indoors is sufficient precautions. If you expect to be stationary, dress much warmer than you would think necessary.