Michigan's not exactly known for its warm, tropical winters, either, but we legally cannot run tire chains or studded tires here.
That said, my Element has performed admirably in the winter.
My E is also 2wd and I'm still running my stock tires 57,000 miles later. I will get new tires before this winter, but in previous winters, the E did just fine.
Truth be told, if you are a competent driver, which admittedly is a rare quality, you don't need AWD to drive in 95 percent of weather conditions you'll encounter on the roads, and really, if you're dumb enough to go out in the other 5 percent, well, not my problem as I'll be home toasty and warm.