I've learned at Wilderness First Aid courses that frostbite makes the affected body parts more susceptible to subsequent frostbite.
I've had some near frostbite experiences when I knew some of my digits, specifically fingers and toes, were really really cold but I was either too busy or too dumb to pay it much attention. "Some of my digits" sounds a lot like an old accounting term used as a depreciation schedule and in a certain respect it applies to the human anatomy: frostbite does indeed cause a depreciation in the ability to respond to extreme cold. I think it has something to do with damage to blood vessels and how that impairs circulation that brings warmth to the extremities. Likewise, it could contribute to arthritic symptoms. I do know that in cold conditions, my toes can turn all kinds of interesting colors. Won't rival the northern lights but could make for interesting campfire conversation.