When you block the sun with you body and form a shadow, the light from the sun is no longer hitting the part of the snow that is in your shadow.
You would think that since no light is hitting that area, it would look completely black. However, there is some light that is hitting the snow in your shadow. That light comes from the sky.
When we look up we see the sun, clouds and blue sky. Light from the blue sky is constantly striking the snow. (Why the sky is blue is another question altogether.)
Usually, this light is mixed in with light from the sun and since direct sunlight is much brighter than the light scattered from the sky, the snow appears white.
When we block the snow from the direct rays of the sun, the light from the blue sky is still illuminating that part of the snow and our shadows appear to be a faint blue.