A mid does well with light snowfall if pitched TIGHT, and if it snows heavily you will need to get out and move snow off the bottom of the sides or they will sag so much you'll lose significant space. this is less of an issue with a Twin Peaks or Betamid, as they have steeper walls - but it still happens, just not as fast. Of course, this will happen with any tent at some point, it's just differences in how many hours you can go between outings if you get a real dump.
My experience is that the real issue with single-wall(nonbreathale single-walls anyway) shelters in real winter conditions is condensation due to poor ventialtion. I made my own sinlge-wall dome with nice big vents in order to deal with this, and it was better than my pyramid or my twin peaks, but still not wonderful. For real winter (as opposed to spring snow camping), I'm a double-wall kind of guy - unless it's just a couple of nights. For a couple of nights you can get away with a lot in terms of moisture. Not so much if you're talking about 5 days or a week.
By the way, my experience is all California mountain winters - other places/conditions may vary a lot.