Anything finely divided has millions of facets that reflect light in millions of directions again and again. Nothing is 100% transparent. So the incoming light gets completely mashed up giving white.

Salt, powdered sugar, mist, a waterfall, ground glass, etc, etc, all the same reason.

Because snow is just a bunch of tiny crystals that scatter all wavelengths in all directions. When you think ice, you're thinking of a solid chunk of frozen water which refracts light the same way, albeit with a lower index of refraction. If the ice happens to be cloudy because of air or impurities, it will scatter more light and appear cloudy, all the way to the point of basically becoming snow white the more impure it is.

Edit: to explain scattering in an ELI5 friendly way, ever played with marbles as a kid? Most of them used to be transparent like glass, but we used to grab a subset and rub them against a rough surface like a pavement to make them opaque. In doing so, they would take a certain color. That's basically how light scattering works, the rough uneven surface doing the work.

Snow is quite different from ice when it comes to the way water molecules are organised. Each snow flake being a weird hexagon reflects much more light per molecule than ice which is much more organized. The more the molecules are organized, the clearer they're seen through.

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Ice, like glass, is clear because its crystalline internal structure allows light to pass through more or less freely. Remember, we see objects by detecting the light bouncing off of those objects. Something clear has a structure that light can pass through instead of bouncing off of, although every edge and imperfection scatters that light a little bit more.

Snow is like ice, except that instead of being made of a big smooth sheet, it's made out of a billion little flakes in all different shapes that pile up against each other at all sorts of angles. All of those edges and angles and irregularities scatter the light so much that it never gets the chance to go all the way through. So the snow is opaque instead, and looks white to us.

Fun fact: If you take a bit of snow and squish it really tightly and warm it a little bit, like in your hand, you can make a little piece of mostly-clear ice out of it. You're basically deforming all those snowflake shapes and pressing them together into a continuous piece, which makes their structure smooth enough to let light start passing through again.

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Snow is mostly air. it consists of crystals which occupy a much greater volume than their overall dimensions. Light reflects off the large surface area of the ice structures which make up the snow crystals creating the impression of 'white'. Ice however is almost all water. If it has air embedded, then it starts looking white where the air is, but the frozen water just transmits light through and does not reflects as white.