Usually, when we get that cold -40 or so it is due to wind chill. I tell women to not wear jewelry or tight clothes. Yes, it looks nice, but frostbite is no fun.
We did cold weather tank warfare training in Germany in 1984 and my face froze. I had blisters all over and the medics put me on indoor duty for two weeks. I hated being inside where it was cozy.
I take no chances when it is cold out. Scarfs and ski masks are your friend in the wind.