The snow and the freezing temperatures are practically characters in and of themselves here. Anytime Shukhov pauses to describe a scene, he mentions the snow and how cold it is. In fact, the cold winter weather is the first thing we hear about after Shukhov wakes up.
The ragged noise was muffled by ice two fingers thick on the windows and soon died away. Too cold for the warder to go on hammering. (1)
The cold and the snow is a constant concern for the zeks, who struggle against freezing to death all day, and the frequent mentions of the cold weather help to hammer home the type of horrible conditions the zeks are facing. The snow also helps to emphasize the desolate and inescapable environment the zeks inhabit. The cold gets in everywhere and the snow seems to go on forever.
The column went [...] out onto the open steppe, walking into the wind and the reddening sunrise. Not so much as a sapling to be seen out on the steppe, nothing but bare white snow to the left or right. (221)
It's fitting that this book occurs in the winter where everything is dead and there's nothing but snow in any direction. The snow here might symbolize the sort of endless sameness of a zek's existence.