No, not really.
The problem is nothing to do with rages. At all.
The problem is using summer tyres. All summer tyres fail to work in the cold and snow, but really fancy summer tyres designed for maximum grip in the summer (like yours and like most tyres made to fit rims like yours) fail even more dramatically.
The small skinny summer tyres on a regular car are marginally better, because they are not high performance summer tyres and have a different compound.
If you put winter tyres on cheap wheels for the 3 months of winter (or any time when the temperature is below 7C), you'd have the fastest safest CTR in existence. The cost is negligible (cheap wheels that you can re-sell if you want, and as you wear the winter tyres you save the summer tyres) and is certainly cheaper than a bump.
More here:
Winter tyres - Civinfo Wiki