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Water
Water is crucial while backpacking in winter because the cold, dry air sucks the moisture out of your body. Drink enough water that your urine stays clear or light yellow.
If fresh snow is available, melt clean snow and pour it through a coffee filter to get rid of the inevitable bits of pine needles, etc. Old snow must be treated like stream water and purified. Water filters are a bad idea, as the water remaining in them after use can freeze and split the cartridge, rendering it useless. Boil the water or use tablets, giving it extra time because the water is so cold.
To melt snow, put a little water in the bottom of the pot first, and it will speed the process up. The water may taste "flat" afterward, so pour it between two pots to put oxygen back in. There is a danger of your water bottle freezing overnight, so either set it upside-down so the ice will form at the bottom, or keep it in your sleeping bag (some people heat the water up first so it acts like a hot-water bottle). As you drink water, put a little clean snow back in to replenish your supply.
Food
Food is the fuel that fires your internal furnace. Be sure to eat plenty of good, high-calorie food, especially before bed. Some veterans suck on candies while hiking to keep their carbohydrates up. Cooking (or any other activity for that matter) takes a lot longer in the cold. Plan simple, one-pot menus that minimize clean up.
Clothing
In winter, Cotton Kills. Jeans, sweats, baseball caps or gym socks have no place in winter camping. If they get wet or sweat-soaked, they will never dry out. Pac Boots are best for snow, but hiking boots can work if the snow isn't too deep. Wool socks with thin nylon inner socks are good, as are polypropylene or other synthetic socks.
Dress in layers so you can add or remove layers to stay cool and avoid sweating. The inner layer should be synthetic long underwear. The next layer is insulation, such as fleece jacket and pants. The outer layer is the wind breaking and water-resistant layer. A hat and scarf are essential to help keep your head warm and shield your eyes from the brilliant winter sun. Mittens are warmer than gloves, as your fingers can warm each other up.
Chemical heat packs that use iron filings come in different sizes, from mitten and boot size to sleeping bag warmers. The big ones are actually cheaper, and they really work. Don't use them on bare skin, or they could possibly burn you.
Hypothermia
Don't be afraid to speak up if you're really cold. Different people are affected in different ways, and there's no reason to suffer. Keep alert of your group's condition. Hypothermia can be diagnosed a lot like a sobriety test. If someone has slurred speech, is confused, stumbling, tired or incoherent, suspect the worst and get them warmed up. Stop and make camp if necessary. Remove any wet clothing, get them in a sleeping bag with heat packs or another warm body and give warm drinks if conscious.