A quiet winter snowfall is quiet for a couple of reasons. First snow does not reflect sound well, it absorbs it so that much of what you would normally hear is muffled. The pores in the snow cover are responsible for the quiet conditions. When acoustic waves travel horizontally above the snow, the increased pressure of the wave momentarily pushes some air into the pores. This air returns to the atmosphere after the wave passes, but some energy has been lost from friction and thermal effects. Over a short distance, this mechanism can significantly reduce the sound energy in the acoustic wave. Secondly, most animals seek shelter when it snows and therefore there are many less bird sounds immediately after a snow storm. I guess you could include a third reason, most people stay inside when it snows.