I was dx'd with Raynaud's back in the 1970's. I don't remember all the tests I had but I remember seeing a specialist, orthopedic surgeon I think. I was tested to make sure I didn't have any of the things like rheumatoid arthritis etc. One thing he did was have me put my hands in ice water and then he watched what happened.
Of course they went red, white and blue.
I have just learned to live with it. I wear gloves a lot and try not to get chilled. I hate getting stuff out of my freezer. Preparing cold food that I have to touch is a problem. My hands go completely numb a lot also.