Vinca minor is the only non-grass groundcover I can think of that will take both your climate, the slope, and the greatly fun abuse . But if you don't mind a grass slope that you do not have to mow...... you might want to explore Buffalo grass (Buchloe dactyloides). It naturally grows short, so no mowing. It will handle your slope. It is heat and drought resistant, happy with your climate extremes, and is a native grass. It is also readily available in seed, since a lot of people are using this as a lawn alternative. And there will be no problems for it under the snow for lots of sledding abuse.

I have a huge steep hill (about 600' X 25') that's currently grass(and weeds)in a 95% sunny location. I'm disabled and my husband keeps trying to kill himself by flipping the mower, so I have to get rid of the grass.

I was thinking about Crown Vetch or Snow on the Mountain but I'm afraid it'll take over my whole yard. I've never heard of Buffalo grass do you think it'll work in my situation? Any thoughts or comments at all would be appreciated. Thanks.