That looks like a bad heater core.epcotbob-
You are not the only Minnesotan with this problem. My Fiancé has a 2011 Cruze LTZ that she purchased used in August of 2012 with the same problem. For the last month I have been reading the other threads that people have started here regarding this issue, in hope that I could figure out a solution. Everything that I have tried has not helped so her car is going into the dealer at 7 a.m. tomorrow. There is no sign of an antifreeze leak present.
With her situation you cannot have the “mode” on anything but full defrost or the driver and passenger windows will completely fog up and the windshield will start to fog (the rear door windows always completely fog regardless of what we've tried). A fan speed of less than 5, with full defrost on; will also result in the driver, passenger, and windshield fogging up. It's been tolerable with only a driver in the car and downright miserable with a passenger. I should mention dangerous as well...
Thanks to the information I gathered from the other threads, I tried cracking a window, varying the temp setting, and turning the a/c on. The only thing that seemed to help was cracking a window. It helped reduce the amount of moisture in the driver/passenger windows but that was it. It would not totally clear them or help clear the rear door windows.
Below are some picture that I took for the dealer after a 2 hour drive with full defrost on, the fan speed varied between 5-6, and the temp varied between 74-80. It is always worse at night and on this particular night cracking a window did nothing. It was just my Fiancé and in the car this night. The windows literally had ice on them. The picture of the passenger side window did not turn out because my garage wall is white but it looked the same as the driver side.
I will report back with what the dealer finds.