My mothers index finger turn completly white when its cold weather. the rest of her fingers seems to have well circulation. why does that happen?

Vasospasm: It is vasospasm also called raynauld's. It is unusual that it is in a single digit. I would wonder if she ever had trauma to that digit.

Raynaud's Phenomenon: Raynaud's is common and occurs when the tiny blood vessel's constrict / spasm and there is a temporary slowing of blood to the fingers. Cold temp. Can trigger it. It can be caused by a different disease like scleroderma or have no underlying causes. Tx includes medications but sometimes surgery which i perform known as a digital sympathectomy is needed.