There is an old Gipsy saying from Hungary: "The cold is nothing without wind."  Truer words were never spoken as the weather could be cold, but no one feels it as much when it isn't accompanied by wind. (As far as the word Gipsy is concerned, it's derived from "Egyptcian," the word an English anthropologist used to describe the Nomads who migrated from nothern India into Europe during the Medieval ages; It was hortened later and became Gipsy from Egyptcian.)

Is Wind a bicycle rider's friend or foe?  Which one is it depends on you to decide. I remember riding 4 Miles to and 4 Miles from my Elementary School on weekdays for more than a half a decade. This resulted in the robust health of my heart, lungs, and especially my thigh muscles that a few years later, even though I was only 65-70 Lbs, was able lift/squat 400 Lbs in our High School Gymnasium in Hungary in 1975-76-77. 

Considering the brutal Chicago Wind Chill factor, it is without question that all riders must use common sense and adequate protection against frost bite!  Common sense should tell you to stay off your bike when the temps fall near or below Zero. But if you still want to venture out into the Cold and Windy City streets, make sure that you dress properly! In one of my previous replies I wrote to use Ski Goggles to protect your eyes and part of your face from the cold. I now wonder if wearing a Ski outfit might also be a good idea to protect your body from the extremes of weather?  Mind you, I did not check the prices of Ski outfits that might be even more costly than your bicycle? 

In closing, this is very important, make sure that your bike's moving parts are well lubricated and your tires are filled to their proper pressure! After each ride on the salted streets or roads, please wash off the salt from your tires and moving parts! Salt dries out the tires and can rust some of the metal parts of your bicycle! A hose wash in a bathtub or outside should help you to remove the salt and preserve your bike's condition.