I have lived in Las Vegas my whole life, and often the only time I'm around snow is when it's for a sporting purpose. I've never lived someplace cold and when I visit cold places I'm often indoors at almost all times. My girlfriend's family lives 45 minutes outside Detroit, for example, and it's plenty cold there. When we visit in the winter (as we will for Christmas), however, we're always inside visiting with family and friends. In Chicago this will not be the case: we're there for a vacation and have no friends in the city.
I have a wardrobe that consists of denim, lightweight sweaters and button-down shirts. The lightweight sweaters already in my wardrobe are all cotton, as is nearly everything else. I have some cold-weather gear that I've used while in the Marine Corps but it isn't really for walking around on the streets (all green and tan, and obviously military in nature). However, I do have some black wool 3/4-length baselayer pants I can wear under my jeans. I also have plenty of wool socks.
I have purchased a heavy-ish wool trench coat for this trip as well as a pair of lambswool-lined, thinsulate-insulated leather gloves, some merino V-neck sweaters to wear over my button-downs and a cashmere scarf/beanie.
Our hotel is the Tremont Chicago, right near the water, and I have heard from many people that not only is it cold as hell in the winter, the closer to the water you get the worse it becomes.
Will my current acquisitions be enough? It won't get below 40°F (4°C) here in Las Vegas for me to test out the coat I've bought or the warmth level of my sweaters with it. I can always shop once I get to Chicago of course, but that won't give me a chance to look for better prices or styles — I'll just be stuck paying whatever they're asking for whatever they're offering.
We will be in Chicago from the 28th of December to the 2nd of January.