The cold-weather setting of "Hunters in the Snow" is a factor in the irritability of the characters, but it doesn't become essential until Rub and Frank are driving Kenny to the hospital. Instead of staying on the road and keeping to their mission, they keep stopping to warm up, and so become absorbed in their own issues instead of remembering that Kenny is dying in the bed of the pickup truck:
The wind was blowing into their faces. The snow was a moving white wall in front of their lights; it swirled into the cab through the hole in the windshield and settled on them. Tub clapped his hands and shifted around to stay warm, but it didn't work.
"I'm going to have to stop," Frank said. "I can't feel my fingers."
(Wolff, "Hunters in the Snow," classicshorts.com)
At this point, Tub and Frank reveal their secrets, which are partially motivating their actions. This allows them to bond, becoming less concerned with Kenny's well-being and more with their own -- they even take his blankets because they decide that he isn't getting any use out of them. Without the cold weather, they might have kept driving and not taken a wrong turn; Kenny's fate rests entirely on the cold weather, which keep Tub and Frank from focusing on the goal.