I agree with Ben. The depth of the snow shouldn't be an issue in Chicago, unless one really likes to ride into snow banks. The streets are plowed and salted pretty well in Chicago... which means salty slush. When the streets aren't plowed quickly enough cars drive through them which means compacted snow and ice.

Any bike, including a folder, with studded tires should do the trick. Due to the salty slush, be sure to clean the bike more regularly in winter... or get a beater bike that you don't expect to last for more than a few seasons.