Just imagine anything that isn't waterproof (aluminum, stainless steel, etc...) with ice lodged in it then melting and
corroding anything it sits on/in, not to mention the horror of salt and slush degrading your brake pads and the mess
that makes.

I rode in weather that bad "once". I ended up spending more time cleaning my bike than I did riding it.
I'll only ride in cold weather when the roads are (and the day is) dry; at least with my road bike.