You know what? I used to be bothered by this. Cold nose a lot. Icy, at the tip. I'd forgotten it. It almost never happens anymore. I seriously think several months of kelp and blackstrap molasses and lemon, and then getting more hip to "high brix" produce changed all that. I also started eating sardines, and getting more sun.
I'm quite sure I was low-thyroid(ish)... but I no longer bother with any labels since retiring my doctor.