Bad snow removal after a 1979 blizzard was the downfall of Mayor Bliandic, the first Mayor Daley's successor.  Since that time Chicago has generally done a very good job on salting and plowing city streets after snowfalls.  The El is somewhat of a different story -- light and moderate snows don't affect it but it can be crippled after a blizzard.

The suburbs usually do not have the amount of snow removal dollars per street mile the city does and this is notable when you cross the city line after a heavy snow.

Chicago usually does not get severe ice storms but they can happen, so be forewarned.

A custom particular to Chicago neighborhoods after snow is clearing a parking spot and then marking it off with lawn chairs, junk chairs, improvised sawhorses or whatever other junk folks think they can sacrifice for this purpose.  Visitors should be advised that one should not park in these spots, lest the incur the wrath (or worse) of the locals.