When the sky is blue, the non-shadow snow is being lit directly from the sun, which isn't blue. The shadows are not in direct sunlight, so they are in fact being lit by the blue sky. Very simple.
Yes, the non-shadow snow is lit by "white" light directly from the sun.
The shadows by definition are not lit by direct light, the light that reaches the shadows is light that's been scattered in all directions in the atmosphere, and blue light is scattered more
than other wavelengths.
Perhaps we should say that, we see the shadow snow as blue-ish for the same reason we see the sky as blue.
Now for the interesting questions:
- do we see the shadow snow as blue-ish on cloudy days?
- if not, is that because the clouds scatter and re-scatter light so much that the different wavelengths are mixed again, more white less blue?