Some years ago a Danish woman tried to ski alone to the North Pole from Greenland (I don't know whether it would have been a first or not, she never got there anyway). One day as she was going to begin another day's skiing, she was attacked by a polar bear. Unfortunately for her, she had packed the .44 pistol she brought along on the sled she was pulling, and she just barely managed to find the gun, and shoot barehanded, but a few shots from this heavy handgun killed the polar bear on the spot. So no doubt this would be possible with a grizzly too.
Fine so far, but when she tried to let go of the pistol, which had been lying in the intense cold for hours, it had frozen to the skin of her hand, and the only way to remove it was to pull it loose with some skin, even so she also got severe frostbite. She called for help on a satellite phone, and was picked up by a plane. Instead of on the North Pole she wound up at the hospital in Chamonix, which has some of the best experts in treating frostbite (due to Mont Blanc and the other surrounding peaks, of course).