You usually dont have to worry as much when you're going from the warm to the cold, but you have to pay attention to your equipment when you come inside after being out in the cold for any length of time.
Best thing to do is to put the camera and lens into your camera bag and bring it in the house, but dont open the bag right away. Just let it sit for about an hour to get acclimated to the indoor temperature. After an hour or so, open the bag and you should be fine.
Make sure you take out your media card before you come in the house. This way you can work on the photos while the camera is coming up to room temperature.
When shooting in the bright snow, you're usually gonna have to play around with your settings because the camera will think everything is that bright, so many times the image will turn out way underexposed.
I'd also Google something like Tips for Shooting Photography in Snow - I tried it and came up with this link
that I thought was helpful