It doesn't get nearly as cold where I am, but I was wearing a lightly lined compression suit, the same thing I wear for skiing. Since it's one-piece, I didn't have to worry about any parts being exposed. I ran with temps approaching zero, and some days with pretty bad wind. On colder days, I would wear a long-sleeved technical top over the top and/or a light vest/jacket. I always wore a pair of very light running tights over the top, just so I didn't look like a total goober When I wore the suit up on the mountain, all I needed was light ski pants and a light jacket, with the top for colder days.

For hands, I was wearing windproof gloves. My hands get warm fairly easily once I warm up, so I didn't need them to be lined. For feet, I wore regular running socks and shoes, though I think something more rugged like a trail-running shoe would be better for snowy days, and maybe two pairs of socks or something a little warmer (sometimes my toesies were cold for longer than I'd like). I avoided running on a couple of icy days, though I would not mind getting some Stabilicers and running more comfortably on those days. I wore a hat until I couldn't stand it anymore, but I would carry it with me anyway just in case. I wore a beanie so it would stay on without having to secure it around my neck.

I think a lined close to the skin base layer is critical in those cold temps, then something on top to break the wind, and something inbetween depending on weather. The hat and gloves make a big difference, and are easy to carry if you decide it's too warm.