Snow and snowflakes are ice crystals mixed with air molecules. The air gaps between crystals, along with the crystals' complex shapes, bounces the light beams around so much that all the wavelengths eventually get reflected out, giving it a white color.
Meanwhile, ice has very little air between the frozen water, allowing the light to pass through with minimal reflection -- although thick ice will eventually absorb the red colors, giving it a blue tinge.
For More Information: