People get around in really cold weather all the time without taking these precautions. If you are not used to real cold or are backpacking, were a Dr is days away and we can assume exposure will be prolonged, here are some guidelines. They come from a Canadian Red Cross/RCMP web site, it is blocked by the firewall of the system I am using so I can’t give you a URL, sorry. The reality is though that in extreme cold (10s to 0F and beyond) you will be bundled as much as you can be, so avoiding hypothermia/frostbite comes down to the quality of your gear and ultimately to access to shelter. In practical terms you are at a greater risk in warmer temps, mid to low 20s. As others pointed out, skin temps well below 25 are needed for freezing to occur. The tricky thing is that you can’t just go by the ambient temperature; wind, wind direction relative to you, and what the wind is blowing all have significant bearing on what happens to exposed skin.
32F to upper 20s: start protecting exposed skin, various balms or zinc oxide work well. You should also remove any exposed piercings at this point (earrings, nose, eyebrow, lip.....) as the metal will efficiently conduct heat away from the site of the piercing (exacerbated by low local blood flow). We saw a lot of tourists in Toronto on very cold days with frozen earlobes (piercings in the upper ear are really bad!!).
Mid 20s to mid teens: cover exposed skin, especially areas with reduced blood flow, cartilaginous tissues, nose & ears.
Teens on down: add double gloves/boots, goggles, thicker balaclava, wind barrier, eventually all your layers and a parka with a good hood (tube opening…).
But really, isn’t super cold why we have cabins, Franklin stoves, fur rugs, mulled wine and significant others……