Oh, I also have cold hands too, so the come on always could have worked for me.
"Are your hands cold? I can warm them up for you."
Although most the time, my pockets came in quite handy. That, or the fact that my long sleeve shirts had a hole for my thumb in the ribbing. That was before they made them into the shirts like they do now. Best style idea as of lately. But hey, like they say "Cold hands, Warm Heart," Or Cold feet, Warm..." Oh, you finish it.