What are possible causes of wrist joint chills?

Go to ER. Chills are usually an indication of ongoing infection and are accompanied by fevers. They occur when bacterial pyrogens enter the bloodstream from an infected area. You should have your wrist examined immediately at an emergency room and x-rays taken.
Not likely a problem. Your symptoms do not make immediate sense to me. Is it stiff? Cold exposure will often make joints feel stiff, cold or chilled, particularly if there is mild arthritis. It does not sound like something to worry about unless there is swelling or mechanical symptoms such as clicking.