When I am out on winter trips, I prefer only to melt snow and boil water for purifying. Water filters don't hold up well in the extreme cold because parts can crack and freeze.
In the last few years, I've been having good success with the SteriPen water purifier, which uses ultraviolet light to destroy microbes, and I think this might be worth a try in sub-zero temps. I have used it to just below freezing, with good results. The biggest problem is in finding batteries that will function in sub-zero temps. Keeping the Steripen and/or battery inside your parka or a warm place will extend battery life by 50 percent in extreme cold.
You will also need clear water to make this device effective because silty or muddy water won't allow the UV rays to penetrate completely through your water bottle.
Here's a snow-melting tip: Wrap a Nalgene bottle in black duct tape, stuff it with snow, and place it in the sun while at camp or rest.
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