When light strikes a smooth flat surface like ice, its visible rays generally pass straight through without their paths being disturbed. This is why glass and ice often appear clear.
When light strikes irregular surfaces, it reflects and scatters in all directions. This applies to snowflakes, which are made up of hundreds of teeny-tiny ice crystals varying in shape and structure.
Because the light that strikes the glass shards or snowflakes is reflected back equally, these rays include all of the composite wavelength colors of visible light (red, orange, yellow, green, blue, indigo and violet), which together, look white.