I'm not a snow physicist, and I did not stay at a Holiday Inn Express last night. However, I saw part of a program on snow today, on the Science Channel.
Snow flakes are actually clear, since they're composed of ice. As the snow falls to the ground and piles up, light is refracted from the snow flake edges in many different directions at once. That refracted light merges, and appears white to your eyes.
And the axiom that no two snowflakes are alike, it true. The number of combinations exceeds the amount of matter in the universe (according to one of the commentators).