To answer this question there are two things which need to be considered – colour theory and refraction.
Refraction is the change in direction of light as it goes from one material to another. It is due to a slight change in speed of the light and it explains why straws look bent in water. When light enters snow, it refracts. This is because snow is made from lots of ice crystals tightly packed together, the important fact here being that these crystals are translucent (light can pass through but not in a direct path – it changes direction).
Additive colour mixing tells us that if we combine all of the frequencies of colours we get white light. When light falls on snow it is composed of a mixture of different frequencies which all refract slightly differently as they enter the ice crystals. Eventually due to refraction, the light leaves the surface of the snow in all directions and hits our eyes. This light is composed of a mixture of frequencies which our eyes detect as white light.