I suppose one could gradually train oneself to ignore the pain and discomfort of the slow freezing of extremities on a cold winter day, and that in itself wouldn't be all that difficult to do over time, but that doesn't do much for preventing the damage of frostbite. Rather, I think one should be more concerned about preventing frostbite as once the tissue is damaged, it may be permanent.
What a person can do is train and condition limbs so there is a well-developed capillary bed and excellent circulation to those limbs. I am always amazed how I can go for a run wearing a thin pair of socks and light runners when it is -20 C and not have to worry about getting cold feet. In my opinion its all about circulation and not pain tolerance.