It’s not stepped, it may not be linear either. It’s probably a curve (but close to linear).
It happens for two reasons:
1. The rubber gets harder, meaning it can’t conform to the road as well. That means there’s less surface contact, and therefore less friction.
2. The tread is not designed to displace snow very well. Snow can be deep, while water on a flat road won’t be. If you can’t displace the lubricant (yes, water and snow are lubricants), you don’t have any road contact, and friction is radically reduced.
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