I spent a great deal of time with the Alaska (Native) National Guard Units in Western Alaska on the Bering Sea. I was the XO of A 1/297th Infantry on St Lawrence Island, and CO of C Company, 1/297th Infantry (The Villages of Shishmaref, Co Hdq, Whales, Teller, Brevig Mission & Little Diomede).
We did most of our training in the winter months, including firearms qualification and training, plus I spent a lot of time hunting with the native peoples.
As to glove, mittens are required. Mittens have to be large enough that you had a light pair of gloves inside. The Trigger finger mittens worked if it wasn't too cold (to about 30 below if you weren't out too long) below that or extended periods the heavier Arctic Mittens were excellent. (I still use both types here in Wyoming. The trigger finger mittens for general winter use, and the arctic mittens for 4 Wheeling in the winter).
Both types can be found in surplus stores or on e-bay at reasonable prices. Normally I don't like military clothing for cold weather, the gloves/mittens listed are the exceptions. I've found none better.
As to firearms, keep them dry, if camping don't bring them in your tent. If extended shooting, start dry and as they warm up (from firing) you can use a light oil (the Military's LAW is excellent). If you're not shooting, wipe off all moisture and oils. Keep them dry.
You're not going to shoot enough to hurt them, if you do, like I said, when they warm up, use LAW sparingly.
It's not really hard to keep them going. Extreme cold (and other weather conditions) effect the shooter more then the gun.
If you're worried about the trajectory changing, use any of the free BC programs out there, plug in your data with different temps to see what it does.
To give you an example (using my I-pod shooter program with my 150 grn SSTs out of my 270 W) at 40 degrees when sighted in at 100 yards the drop at 600 yards is 9.9 MOA, keeping every thing the same, if I shot at 40 below the drop at 600 would be, 9.7 MOA. So that's not really as much of a problem as one would think. Of course different rounds react differently.
CPT USAR Ret
USAMU Sniper School Oct '78
Distinguished Rifle Badge 1071