Were you a Norwegian fisherman or Inuit hunter, both of whom frequently work gloveless in the cold, your chilled hands would open their surface capillaries periodically to allow surges of warm blood to pass into them and maintain their flexibility. This phenomenon, known as the hunter's response, can elevate a 35-degree skin temperature to 50 degrees within seven or eight minutes.
Other human adaptations to the cold are more mysterious. Tibetan Buddhist monks can raise the skin temperature of their hands and feet by 15 degrees through meditation. Australian aborigines, who once slept on the ground, unclothed, on near-freezing nights, would slip into a light hypothermic state, suppressing shivering until the rising sun rewarmed them.
You have no such defenses, having spent your days at a keyboard in a climate-controlled office. Only after about ten minutes of hard climbing, as your body temperature rises, does blood start seeping back into your fingers. Sweat trickles down your sternum and spine.