Regarding driving in the winter... I drove for two years in Colorado, where we would get 400+inches of snow every year (13x as much as Chicago got last year) so this comes with the disclaimer that I'm somewhat used to it. (Then again, I also spent the last four years driving in Florida). On the one hand, where I lived in Colorado they plowed every road thoroughly... whereas here they only plow the main roads. This can make driving on back roads difficult, and you need to stay in the center because the snow builds up in the middle and it's tramped down where tire tracks push it down. I don't know if they have any such courses in Chicago, but my first winter in Colorado I took a winter driving course (not like in a classroom... you use their cars and drive around on an ice course)... it was a ton of fun, and it was also really helpful, so if you're going to have a car it's definitely worth doing.
A car isn't necessary at all. If you end up living in Regents, you're just a few blocks away from Treasure Island, and can walk/take a bus just about anywhere you need to.
That having been said, I have a car, and I'm going to keep it here. I like to buy a few weeks worth of food at once (too much to carry on a bus), and frequently shop at places, like Trade Joes, Target, Costco, that aren't in Hyde Park. When I needed to get a suit downtown, having a car made it infinitely easier than taking buses at random times of day would have been. When it's 11PM and I realize that I left something important in my locker, it's nice to be able to hop in and easily get it. I also get sick on buses, so I usually drive to school in the mornings.
But these are all conveniences that you don't need. I think they're worth it. I live in university housing, not regents, so parking is about 1/3 the price of regents. If I had to pay the regents price, I probably wouldn't have a car.
If you're unsure, you can always bring a car, and if, by winter break, you don't feel you want it, just drive it home over the break.