Keep things covered. There are no points to be earned for either style or machismo in extremely cold conditions.
Also on cold days, identify the wind direction, and choose a route that covers the most distance in that direction early in the route. Otherwise, there is greater risk of working up a sweat running with the tailwind and then having it turn into a cold sweat once you hit the headwind. If wearing multiple layers, an outermost layer with a zipper is a good idea. Zip and unzip as necessary to prevent overheating, ex. unzip while climbing a hill or running with a tailwind, zip up on the descent or after turning into the wind.