Have spare batteries somewhere warm (an inside pocket close to your body heat).
Make sure that if you drop anything, you don't have deep snow under your feet! This is a good way to lose even a lens!
A car is a good place to defrost your camera, when the inside air is dry. There is very little condensation. Inside air in buildings is much more humid! So when having a break, leave the camera outside. When going inside with the camera, bag it airtight, then there's no condensation problem. But if your camera gets steamed up, let it dry in peace. If you take it out when wet, you can break it!
Lapland can offer magical colour shows during polar night in daytime.
There isn't that much light, so make sure your exposure is correct and you should use a tripod in the daytime.