Why is snow white and ice transparent?
Ice is a monolithic crystal whose structure is very stable and homogeneous. Snow, on the other hand, is a bunch of small crystals - snowflakes - whose shape itself is much more complex.
Light is a bundle of photons, each of which can have its own color. Actually, light is both a wave and a particle at the same time, but that's a separate topic. If such a bundle of all the colors of the rainbow hits our eye, the brain interprets this as white color. We'll consider the situation when white light falls on snow or ice.
So imagine a clean piece of ice. A bundle of white light falls on it. Since ice has a homogeneous structure, this bundle can uniformly refract in one direction and exit together just as uniformly. Thus light preserves its structure and we see what's behind the ice, which means it's transparent.
In snow, however, each snowflake is already not so transparent, but they're also chaotically layered on top of each other, and there are air gaps between them. A bundle of photons enters such a mess of crystals, and then each individual photon can reflect or refract in its own separate direction due to a bunch of obstacles in the form of individual crystals in its path. Therefore, at the exit we get a bunch of photons that have chaotically changed their original direction and are flying in absolutely different directions.
But nevertheless, all colors are preserved - they're just mixed up. All this hits the eye and the brain similarly combines this into one white color. But nothing can be seen behind the snow anymore, because the original structure of the light bundle is lost.