My summer tires "failed" in frigid temps. Let me explain (and I consider myself lucky). I parked on some snow, in gravel, maybe 2-3 inches, I guess there was some ice, and it was on a very slight slope, but very slight. I parked very close to my wooden privacy fence, to test out the parking sensors and for fun. E-brake on, in park, got out, locked up and walked away to stand nearby for five minutes or so.
I heard a sound, my heart sank, the car slid into the fence, but luckily it only moved about 2-3 inches because I parked so close, and luckily the fence held without any damage, and luckily I didn't have a front plate on yet, and it just barely touched the plastic plate holder area - literally no damage, but a SIGN, a WARNING from the motor-gods. I took it to heart and ordered a set of winters. Eff that noise.
I guess the heat from driving warmed the snow enough to melt, then ice and there was zero traction once it was ice. I also know there is zero traction on icy surfaces from driving it, but parking on bumpy gravel in the icy snow on only a slight incline was what did me in. I absolutely do not trust my summer tires in the cold and ice.