There are no issues going from warm to cold. Don't make any attempt to keep the camera warm when outdoors, just let it get cold and leave it cold until you are finished. I always have a second battery in a warm pocket next to my body, and swap them out whenever it is necessary. Before you bring the equipment indoors, put it all in a plastic bag of appropriate size (I often put the whole camera bag into a garbage bag) and let it warm slowly sealed up from the indoor humidity.
It is far more important to worry about YOU and your ability to photograph in cold. Hands are a big problem. Gloves that allow you to manipulate the camera controls won't be very warm. Cold cameras and tripods suck heat very rapidly. My solution is to wear thin gloves inside warm mittens. Take the mitts off to work; the thin gloves provide some protection; then put the mitts on again to keep warm.
Your camera will do just fine in the cold. YOU will need to stay warm if you want to enjoy photography in the cold.