I live in northern Wisconsin and drive a 2013 Cruze and this happened to me at the worst time as well, you have my sympathies. There is a poorly designed gear that usually becomes brittle and can break in cold weather (mine happened the first winter I owned it). Before getting the gear properly fixed, I did use the DIY method just to have defrost. Just don't touch any of the vent direction buttons once you have placed the screw/golf tee in the gear area, or you risk having it fall out (I learned that the hard way).

The part itself is very inexpensive, but if you take it to a shop, the labor is where the bill will add up. It requires much of the dashboard to be disassembled to work on with any comfort. Fortunately, my dad used to be a mechanic back in the 80s, so we were able to fix it ourselves. Granted, it took 7 hours on a Saturday, but it was a lot better than paying for the labor at a shop. I am sure someone more skilled could do it in less time.

Hope you can get the defrost running soon. GM cut that corner way too sharp and it is a huge safety concern for people driving in frigid climates.