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.