My right side thumb gets cold it seams as though it is not getting proper blood flow. What can I do what kind of a specialist I go to.?

Hand surgeon. I would need a little more info to properly guide you. It sounds vascular. I would first start with a hand surgeon and consider a vascular surgeon or neurologist.
Blood flow to thumb. Good place to start is with your family doctor for a check up, and then see what the advice is as to what to do.