A lot depends on what you're doing in the snow to begin with. The clothing that keeps you warm when you're sitting will cause you to overheat (and sweat, and ultimately get cold) when you're moving.
Because of the way your body works in the cold (pooling blood to the core to protect vital organs, etc.), regulating your core temperature will often do as much to keep your extremities warm as anything. I generally pay a lot more attention to the jacket/coat/parka I'm wearing as a result. And after that, more attention to boots, gaiters and gloves/mittens. "Pants"? Meh. I find that I can get by with everything from old BDUs (not ideal) to milsurp wool (when it's really cold). When I plan on walking most of the day, I EXPECT that I'll be a little chilled when I start out (knowing that I'll warm up). If I need to, I'll shed a layer of jacket/coat/parka so that I'm not TOO warm. If I stop, I'll layer back up, but not so much that I find myself sweating. Though my wife is from one of those "northern" states, she still hasn't quite figured out the layering piece and still insists that she be toasty warm every step of the way. Consequently, she's almost ALWAYS uncomfortable - either too warm or too cold.
Ultimately, you need to be able to adapt to the conditions. What I wear deer hunting in November isn't what I wear coyote hunting in February.