Snow, which is made up of millions of ice crystals and air pockets, reflects all of the wavelengths of light in the visible spectrum. When combined, the reflected light wavelengths create a white color. All objects in the world get their color based on which wavelengths of light they absorb and which ones they reflect.
When a beam of light hits a pile of snow, it bounces off each reflective surface on the individual ice crystals and through the air pockets, eventually reflecting back out. Because snow reflects each different light color in equal measure, no one color is more prevalent than any other. All of the colors that enter the snow are the same as the colors that come out.
The color of snow is often different from the color of an individual ice crystal because ice is translucent. When a crystal is isolated, some light passes through and some is reflected. When the ice crystals are packed together in a snow bank or snow pile, the light behaves differently and creates the white color.
Different types of ice, like the ice that is found in glaciers, also come in different colors based on density. Because light can move further into ice than snow, the red end of the light spectrum dissipates and the blue wavelengths are reflected, giving the ice a blue color.