The thing to know about dealing with cold is that your body will focus on warming your core in response to the cold. So, your feet and hands will be the first thing to feel bitter cold. Once your feet get cold youre finished. It saps your will to want to do anything else but get warm.
So, socks and gloves are the two most critical pieces of clothing. If it gets below 0, you want to be wearing two pairs of socks instead of thick fluffy ones. You want gloves that have two layers of protection (inner shell, outer shell). Single layer gloves won't cut it if you spend longer than 30 minutes outside.
Also, my experience in Chicago is limited. But my memory is that all the things I wanted to do were located in a few places. So, I was able to get away just relying on cabs/ubers. It never felt unsafe.
