Snowflakes are crystals of frozen water. Water and ice appear clear or slightly blue in large volumes. Snow is white, because of the way light interacts with snowflakes and the air molecules packed between each snowflake.
Water, ice, and an individual snowflake may appear transparent or clear, but water actually is translucent. The difference is that light can pass through a transparent material unchanged, while it is bent when passing through a translucent material. Light hits a snowflake and is bent and scattered across the spectrum by the facets and imperfections in each crystal.
Snowflakes scatter all frequencies of visible light, so the net effect is to produce white light, but deep layers of snow or compacted snow may appear blue. There is little air between crystals in compacted snow or ice, so there is less opportunity for light to be reflected. Thick layers absorb enough red light to cause this snow to appear blue. Snow also can appear blue if it has a layer of ice over it, which can reflect back the blue of the sky.
Ice is the word for the solid form of water, regardless of how or where it formed or how the water molecules are stacked together.
Snow is the word for precipitation that falls as frozen water. If the water forms crystals, you get snowflakes. Other types of snow include rime and graupel, which are ice, but not crystals. Bottom line, frost is ice, ice cubes are ice, and snow is a form of ice.