What is the sound of teeth hitting each other in cold weather called?

The most common and idiomatic word to describe this situation is chattering.

From WordNet:

chatter: click together repeatedly or uncontrollably

"Chattering teeth"

Chatter is the word you are looking for:

Chatter (teeth):

• If your teeth chatter, they knock together repeatedly because you are very cold or frightened:
  • I could hardly talk, my teeth were chattering so much.

Cambridge Dictionary

I've also heard Clatter used for this.

A continuous rattling sound as of hard objects falling or striking each other:

From Google books the following quote

“'Who are you?' I asked through clattering teeth. I was shivering from head to toe.