Let's go over what we know about color. Sunlight is made up of lots of different colors all mixed up together. Light can either be reflected or can pass through things. Different colors might be reflected or transmitted differently, too. An example of this is a prism. A prism takes white light and transmits each different color slightly differently. This ends up spreading the white light out into a rainbow. Not surprisingly, a rainbow is made when light from the sun is transmitted through drops of water differently, causing the different colors to separate.

For snow to be white, it means that it must be reflecting all the different colors of light equally. For ice to be clear, it is transmitting all the colors of light equally and not reflecting them back to your eye. To understand where the difference comes from, we need to think about the structure of snow. Lets start with ice. Ice isn't really as transparent as a pane of glass. If you look through an ice cube, everything looks kind of murky. This is because the ice is bending the light a little bit -- it doesn't pass through the ice in a straight line -- and so things get blurry. Snow is made completely out of a bunch of tiny flakes of ice. So when you are looking at a snow bank, you are looking at a bunch of tiny ice flakes and a whole bunch of air that fills the spaces between the snow flakes. Since it snow flake is ice, it will bend light passing through it slightly. This light will hit another flake, then another, then another, and bounce around randomly from flake to flake until it eventually comes right back out again. Some of the light does get absorbed by the snow but a lot of it comes out.

Since snow doesn't distinguish between all the different colors of light, they all get reflected back and so the snow appears white. So here is a question for you: What happens if you take an ice cube and you start scraping off a pile of ice flakes? Would the pile look clear like the ice cube or would it look white like snow? Actually, if you have a really large chunk of ice (for example, a glacier) you will notice that the ice looks a little blue, not clear. This is because ice absorbs red light better than blue light. As light travels through the ice, it has less and less red in it but the same amount of blue, so it appears bluish.

I believe the difference is that snow is made up of a bunch of small water crystals where big blocks of ice are not. All the crystals in the snow would tend to reflect the light in all sorts of directions with the net effect that a lot of the light that hits a pile of snow is reflected, making the snow look white. With ice, more of the light is transmitted through which makes the ice seem colorless.

An even more dramatic example is the difference between diamonds and graphite, both are carbon. Diamonds have a crystalline structure and tend to reflect light in interesting ways. Graphite does not have the same crystal structure and looks black.