Long distance backpackers commonly wear non-gtx shoes in lots of snow; I've done so on three trips, most recently walking through a whole lot of snow covered parts of Montana in June 2011.
Making this work is in part about hiking "style" (keep moving, steady metabolic heat generation), in part about the magic of wool socks. VBL socks are a good backup; bread bags make a low-durability backup option that's very light, plus are very nice to use in camp to wear dry socks inside of wet shoes.
Really, I think some cold-weather scenarios are BETTER handled by non-gtx shoes: walking in lots of snow during spring thaw in particular. You can find yourself walking a great deal in lots of water, just no way to keep any footwear dry. And if your wet footwear does freeze at night, it's easier to crack shoes open to get feet into in the morning than frozen boots, and less thermal mass to warm up at the start of the day.
I wouldn't want to do any serious mountain climbing this way, nor be tied to the schedule and hiking style of others who go about things differently, but for solo hiking or hiking with folks who are similarly shod (and experienced), I like non-gtx shoes for most if not all conditions found in 3-season backpacking.