What purpose does "Mir ist kalt" serve, why is it used instead of ich bin kalt?

Answer 1

it depends on where you use it. Mir ist kalt isconsidered more polite in some provinces, epeciall in the east. In the west provinces though,
ich bin kalt can be used in polite society.

Answer 2

Several languages have these two constructions. The first is a temporary condition due to the weather. The second can either refer to a sexual or permanent condition (as in English, "she's so cold-hearted." Or "he's cold," said the coroner. However, the second expression can be used in casual conversation.