Advice appreciated for shooting in extreme cold

I will be in Iceland middle of next month and would appreciate any first hand advice from anyone who has been shooting in similar conditions.

Specifically

• Should I bother with rain gear for the camera?
• Is battery drain more than what one would expect?
• I'm taking a Gitzo traveller tripod 4 sections GT1524T so a little compromise perhaps on stability of a 3 section for the lighter weight
• Likely taking a Nikon and Leica body with 2 lenses for each system
• FL of primes 15, 21, 35, 50

Thanks for any feedback you can provide.

David
Australia