Agree about the 35mm clearance at minimum. Regarding 3), cold weather and/or slippery surfaces are basically not huge issues. They can be addressed with layered clothing and studded tyres. If roads are plowed quickly, OP shouldn't have much of a problem. If not - well, we have MUPs that are plowed after the roads are clear (they've promised an upgrade for the MUPs with highest traffic though). This past winter I spent 2 hours "riding" a commute that usually takes me 35-45 minutes. There was snow up to hub level in banks on the MUP. I had to push the bike on several occasions. My winter tyres are Nokian W106s, they're great for icy roads with little snow, but not so great in deep snow. xc skis might have been good that day.

The good thing about snow is, you get traction. If the conditions are really icy, or the snow is hard packed and polished, you'll need to learn to brake primarily with rear brake and NOT lean into curves.

--J