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You are at the whim of nature much more than any other season. Weather can turn rapidly at elevation, conditions vary weekly, and yea it's cold which means if anything goes wrong you're in double trouble.
In the North East you have to pack for everything depending on what you're doing. An inch of snow at the trail turns to a foot of fresh powder 4000ft. Hiking poles are a must in the snow, especially if you're breaking trail. Microspikes are a must, snow shoes probably. Layers are even more important now, make sure you have enough to keep you warm if you're standing still. Do your best to avoid getting your clothes sweaty, and bring spare base layers if you're going deep. Always pack extra socks!