My cold hands and feet (and my fingernails and the tip of my nose would go blue/purple!) were resolved when I cut wheat/gluten out of my diet.
I don’t know how/why that would be, but gluten seems to have some negative effect on my circulation, which I believe is why my extremities would be icy cold.
I had a thermogram done for screening of my breasts (I don’t do mamograms) and the thermographer commented on how icy cold my feet and hands were. Certain fingers were really cold! My follow up 4 months later (after cutting out wheat) showed fairly solid improvements, and I don’t find I need to drink hot tea constantly to stay warm, or wear 2 layers more than everyone else.