If ice is clear, then why does snow/shaved ice appear white?

Question

If ice is clear, then why does snow/shaved ice appear white?

In:

Answer 1

The same reason that smooth glass is see through, but it you make a surface rough, it scatters the light as it crosses that surface, and you get the frosted effect.

In fact, if you put sticky tape on a pane of frosted glass, it effectively creates a smooth surface again, and you can see through the glass.