Plastic/composite stock, they'll last longer in extreme temperatures. Wood, while serviceable, will not hold up as well to a well-constructed synthetic. Metal fatigue & stress due to cold will be a great problem, as it was in WWII, firearms with lots of stamped metal & small springs have a good chance of shattering. The reason that polymer-framed weapons such as Glocks and Steyr AUGs were adopted due to specs for function in extreme sub-zero conditions.
The Russians, Finns and Germans used sunflower oil as lubrication in Actic Circle warfare in WWII. Second choice was nothing at all. They used mostly bolt-actions and LMGs with rare access to plastic weapons (mostly MG34 & MG42).
I also believe that their solution for frozen weapons was "fresh" urine.
The only other "cold" war fought recently was in Korea, using WWII surplus weaponry, but it wasn't as cold as Russia.