An alcohol stove like a Caldera Cone works fine for cooking in the winter. It would use a lot of fuel if you had to melt snow, especially if its for two people. If its cold enough, canister stoves perform pretty poorly to not at all. At that temperature alcohol doesn't volatilize either, so it won't start with just a flame. What I do is put a little alcohol in the primer ring, put a little piece of paper in the alcohol (like a paper match, or a piece of paper as big as a thumbnail). Light the paper, and in a few seconds the alcohol nearby is warm enough to volatilize, and the vapors catch fire, pretty soon the alcohol in the stove is warmed up, and catch fire. This process takes about 30 seconds, so its no big deal.
Put something under any stove, like a piece of thin plywood, metal tent stakes, a piece of bark, or a commercial stove stand, so the stove doesn't melt into the snow. I use a 1.9 L pot, or a 900 ml pot, depending on if I need a fry pan.
Put a little clip on the end of a sky/hiking pole, so you can lower a water container into a stream using the pole, to get liquid water. It might be otherwise out of reach, if the snow is 4' thick.
Of course, a gas stove like a Dragonfly is the blowtorch of stoves, and can melt a lot of snow for water, but its heavy.
blog post on this topic: http://backpackingtechnology.com/food-and-cooking/can-you-use-an-alcohol-stove-in-the-winter/