If you see this sign, you can't park between 3am & 7am period. So don't. Seriously. You'll be towed faster than you can say "Where's my car?" 107 miles of Chicago streets are covered by this restriction.
This sign is a little more ambiguous. One story in the Tribune said it means you can't park if there are more than 2" of snow on the ground, and another said it means if more than 2" have fallen you'll be towed. The City of Chicago says it's when there are at least 2" of snow on the pavement. Safest bet: if there's more than a light dusting, don't park. There are 500 miles of streets that have this designation.
This one's the double-whammy. From now until April 1 don't park here between 3 and 7am, AND don't park here if snow is over 2" deep.