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In my experience it's pretty much just about warmth, what with the whole temperature thing being a bit low in snowy conditions. Sleeping bag, extra clothes, all that jazz.
Though now I think about it, a big thing is sleeping mats. I tend to take two when I'll be sleeping on cold ground or directly on snow. It really does suck the heat out of you.
Water is easy to find, just grab a pan full of snow from right outside the tent and boil it up.
Some tents take snowfall better than others. The full multi-pole geodesic ones are generally best at it, while the tunnel style less so. Exceptions to every rule though, and it has to be pretty heavy snowfall that you couldn't just wake up and bash off any bits that are really sagging in the night.
I usually try to dig a hole in the snow so I'm pegging my tent into proper ground. I'm from the UK and we never get enough snow to make that a particularly difficult task.
Pic related is about as bad as I've seen it.