I agree with tinman that it is mostly psychological. I moved from sunny San Jose, CA to Anchorage, AK at around New Year's 5 years ago and had no problems continuing to run every day despite a record streak of cold weather that hit right after I arrived. For about 10 straight days, the thermometer never went about 0 F. Figuring out the clothing adjustments needed along the way, I was running in -20 F weather even though I had never experienced about sub +20 F weather and probably never ran in below freezing weather before then. Winters in San Jose, it's cold when the lows get into the high 30's F.
That's why I think it's silly when people are talking about cross country races in colder weather... they discount the chances of fair weather folks way too much. There is definitely acclimatization that occurs when running in the heat, but not the cold.
That said, I think just looking at the pictures from NCAA cross last fall, many people were underdressed for the conditions. You shouldn't need to keep turning your head, like Hall did, because your ears are freezing. And you shouldn't have to be like a frozen popsicle like I read Ritzenhein was like after the race. They were definitely not optimally dressed, even considering that they were racing. Temperatures like that (around 20F) should be very comfortable - just look at cross country ski racers, who put out similar efforts in the cold. 20F is very comfortable in a racing ski suit and wind briefs, and a light underwear top layer. For running races at those temperatures, some tights and long underwear under the racing singlet, earband or light hat (e.g. Swix), and light gloves (e.g. rag wool) would keep you plenty comfortable in those temperatures in a race. It doesn't get difficult to ski race (with layering adjustments)until it gets below about -5F. Training is easier to do at even colder temperatures because you can bundle up more.