What about something like prairie plants? They generally grow in areas that experience a wide variety of temperatures, and ought to thrive in your conditions. It's worth checking the hardiness of each variety, as you're going to need some tough cookies for -20!!
I think when you have real temperature extremes like that, getting the soil right is really, really important. I would hazard a guess that this could be why grass is struggling - very hardy varieties should be enjoying those conditions. You may have very compacted earth that needs digging - and you may need to add drainage (grit) and organic matter (compost).