The layer advice is very important. Even when it is mildly chilly, tie a windbreaker with a hood around your waist, and it’s there if you need it.
For races, if you get into those, there is a problem in the cold before the start where you have to wait, yet don’t want to leave good clothes behind you. One good solution is to cut arm and head holes in a plastic garbage bag and use as a jacket, then discard that at the start.
I ran through more than 20 Vermont and upstate New York winters, nearly every day, so it can be done. When it is really cold, and your lungs hurt, breath through wool, either a ski mask hat or a muffler around your neck.
For the guys, when it get really below zero, and especially if there’s a wind, be sure to stuff some plastic or a wool miten around your privates, or you’ll know the meaning of real pain!
Also a good idea to slather some Vaseline on your face, and even on your thighs and bottom (in case you have to make a pit stop). Although, for some reason, my feet never got cold, Vaseline on your feet not only will help but will help avoid blisters.
Also slightly off topic, but important, in the shorter winter days, it is vital to be seen, so get some bright orange vests, headbands, armbands as even on cloudy days it is hard for drivers to see runners. I used to look like a Martian, but with all the reflective stuff, I could surely be seen! If you have to run after dark, carry a big 4-5 cell flashlight. Not only does that alert you to drivers, but I found when some would not dim their lights, if I flashed it for a second at them, they usually dimmed them.
It should not have to be said, but a reminder to those who may not know: Always run facing traffic!!!