Rule of thumb: you should never be where the temperature is measured with a -.
I've run gravels in the snow in mid +20 temperatures with no problems from brittleness, but the big square tread blocks might as well have been slicks. Actually got so stuck on flat ground that I got out of the car with the car idling in 1st gear and helped my co-driver push. Rear tires just spun at idle...
I got going by throwing on my spares (I carried two) which were worn, and therefore had natural, gravel-cut sipes in the tread blocks. They were much less bad. For the next stage, we just put chains on. Nobody thought to bring snows to Arizona...
-Dave