A motif is a recurring structure, contrast, or literary device that is used to develop a theme in a book. A symbol is an object in the story that is meant to represent a deeper meaning. In this case, snow is more appropriately used as a symbol rather than a motif, as it is not something that recurs throughout the story, but is basically prominent in only one section of the book.
In Section 6 of the story, Elie, his father, and the other prisoners, are forced to escape the camp on foot, run many kilometers through a cold and snowy night, and finally seek rest in an uncovered shelter where it is snowing heavily. Many are dying all around him, from severe exhaustion, starvation, and the cold.
Heavy snow continued to fall over the corpses (90).
In this case, the snow provides a peaceful contrast to the chaos of the run and now the death that is happening all around. Though the bitter cold is actually speeding up death for many, it is as if the snow is providing these victims the ability to simply fall asleep and never wake up. As the snow covers the corpses, they are forgotten. If you look at this symbolically, think about the snow, a white blanket, covering forgotten men who died for nothing. Also, the white snow is a stark contrast to the red blood which would have been the result of these same men being shot to death (many while running through the night). This cold induced, peaceful, sleep-death heightens the sheer physical and emotional exhaustion Elie is feeling as he slumps down next to his father, each promising to stay awake while the other sleeps. The reader can sense the quiet, calm, acceptance of death in this scene.
A thick layer of snow was accumulating on our blankets (96).
Later, at the end of this section, the prisoners who survive the selection are led out of the camp with blankets on their backs. They are not allowed to sit or bend over. As the snow accumulates on the shoulders of each prisoner, they eat it off each other with their spoons to quench their thirst. Here, the same symbol that brought a peaceful death to many just pages earlier, is bringing a small amount of nourishment to those who still live. The soldiers laugh at the spectacle, but once again, the scene is viewed with a sense of silent acceptance.
Snow, in this section, can be symbolic in many ways. It is cold, paralleling the cold hearts of the soldiers. It is clean/white, symbolizing the innocence of the prisoners. It is silent, representing the final acceptance of a fate brought on by so many months of fear and abuse. And, it covers everything equally, symbolizing both the lack of personal identity (especially in death) of the prisoners, and the worldwide secrecy of what Hitler was accomplishing in all of his death and concentration camps.