I would agree with your general description: is physical freezing - usually of water or other liquid - or freezing cold. It is more objective (you can measure a freezing point). Exception: when used metaphorically as in {} which is probably close to the English "blood-curdling".
It can also be sometimes used when ice covers something e.g. []{} - a road that has iced over.
is freezing in terms of feeling/your body's response as in "it's so cold I can't feel my fingers". It is more subjective. It can also be used to refer to parts of the body, e.g. []{} - fingers stiff with cold.
So it makes more sense to talk about "[]{}" than "", and I think it's possible to say []{} when the temperature isn't actually below freezing.