The old ice cream brain freeze feeling, only it doesn't stop till you stop cycling...
I get by with a snood under my helmet pulled down to my eyebrows and another from below pulled up over my nose. But then I've not cycled in lower than -3C, I think.
Maybe you need a full face helmet and goggles? Money aside...
Stoneware is the worst. I have 50+ year old hand me down ceramics that seem tough as hell. New stuff ends up chipped, cracked and broken far too soon.
I'm certain that modern tableware is built to fail compared to what it's possible for modern ceramic science to create.