Just a couple of winter running notes:
I like to wear socks on my hands in lieu of gloves or mittens, which always get my hands too warm when running. With socks (just short ones), I can take them off and roll them up in my hands and keeping them like that is just about right when it's 0F to 10F.
In the teens and twenties, I like to wear a cap with a visor, but not a baseball cap. Since you get hot when you run, if you trap the heat with a knit hat or even a thin baseball cap, you may overheat quickly. I find a visor cap allows the heat to escape. I start with a hood pulled over my hat for the first mile or two and pull that back as I warm up. The cap keeps my forehead from getting exposed and sweaty - a bad combination in the cold.
And a note about extremes. Health experts advise against exerting yourself in extreme temperatures. I avoid hard workouts in the extemes, but won't avoid running an "easy" workout when it's 100F and humid, or 15F below 0 and windy - I'll just make sure I'm taking it easy. If there's no enjoyment in it at all, you've probably found your lower (or upper) limit.
Just getting out on a running path and seeing others out there enjoying themselves is what made me realize I was placing stoopid restrictions on myself.