Dress in layers when heading out to do winter photos and don’t forget your gloves instead of mittens! Also, protect your camera from the winter elements by climatizing it to the cold slowly. Put your camera in your camera bag and put near the front door or in a porch that is colder than the rest of your house, then move your camera bag to the car so it is isn’t directly exposed to the cold, but it is definitely getting colder. This prevents your camera from fogging up when you take it out to start shooting. It is now time to take your camera out into the cold. If it is snowing cover up your camera with a clear plastic bag to protect it from the wet and cut a hole for the lens to fit through. Once your camera is cold you want to avoid getting it warm and then cold again because your lens will fog up similar to your eyeglasses. Also, the condensation is not good for your camera.
Having an extra battery is a good idea. Your camera battery won’t last as long in the cold so have a back up one in your pocket where it is warm.