My right arm and hand are quite cold, the left arm and hand are normal temp.

Consider these 2: Look for a problem in either the peripheral nervous system, such as a nerve compression in the neck, or in the circulatory system. If your blood pressure is roughly equal in the two arms, it's more likely a problem with input from the nervous system (e.g. Via a compressed nerve) indirectly affecting blood distribution by small vessels.

Vascular dz: Consider a subclavian artery stenosis (narrowing) of the blood vessel giving blood flow to the arm. Blood pressure should be lower in the cold arm than the warm arm. Reflex sympathetic dystrophy is another consideration but usually has pain. This should be evaluated with a ultrasound study of blood flow velocity in into and through the arm. If present other vascular disease must be considered.