You should be issued with everything you need but there is a few extra things that will improve your comfort. On the initial digging try to wear just base layers & waterproofs as you soon build up a sweat(Make sure you have dry kit to get into afterwards). You can get insulated 'marigolds' (for packing fish etc) which are great for your hands, try to avoid using your mountaineering / skiing gloves they just get saturated.
You will probably get shovels but often they aren't the best tools in isolation. A really good saw is worth the weight -this need not be a snow saw, my Silky 'Bigboy' is an excellent tool for cutting snow as well as wood. I went on one trip & we spent about four hours digging the snow hole as the snow was like concrete, a decent saw (which we didn't have) would have been a massive advantage. Consider digging a cold well if its well below freezing.
You need a bivi bag to stay dry & I would recommend two mats (one closed cell & one Thermarest on top, which can be 3/4 length) as you lose loads of heat to the ground. Tent boots are great and down ones are very light.
For cooking its worth waterproofing a square of cardboard to raise your stove (or carry a small piece of wood). You may not have the choice but petrol stoves work better than gas at sub zero temperatures. Light is usually candles & they work fine. Enjoy!
