The question is: why does snow appear white, even though ice (and snowflakes are ice) are see-through? It has to do with the surfaces of the snowflakes, and how many of them there are, and how randomly they are arranged inside a pile of snow. Remember the picture of the guy looking through a piece of ice and we could see his face? That’s because the light rays coming from his face go through the ice mostly unaffected, then they go into our eyes and we “see” him.
When light rays go through something they can either: transmit (go through), reflect (bounce off), or be absorbed. (There is also something called refraction, but we’re going to ignore that for now.)
In the figure above where a ray of light goes through a block of ice, we see that a little of the light might reflect off the surfaces. In the case of snow, when there are a lot of surfaces, so much reflection happens that rays of light end up going every which way, so they all get mixed together by the time they get to our eye. And “mixed together” colors are white.