Light, be it from the sun or from the light bulb is a combination of the different colors in the rainbow, colors that can be broken down in order of their wavelengths. When all colors combine in equal proportion, with no color range dominating, the light produces white color.
Most objects tend to reflect only some of the light falling on them, absorbing the rest. The color any object spots is the color reflected by the object. For instance, grass absorbs all the colors of the rainbow except green, and this is why grass is green.
However, the same is not the case with snow. Snow reflects and refracts all colors of the rainbow equally without any color range dominating, thus appearing white.
Snowflakes are actually molecules of water. The water vapor in clouds turns into moisture by the normal process of condensation. When temperatures are normal, this comes down as rain. However, when temperatures are below freezing point this moisture freeze and form ice crystals. Snowflakes form when many such ice crystals combine.
The ice crystals thus formed always have six rays, but the designs are always different and thrown together chaotically. No two snowflakes have ever found to be exactly alike!
A beam of sunlight entering this snowflakes is quickly scattered by these myriad ice crystals and the air pockets between two crystals, so that most of the light comes back right out. Whatever light leaves off the back of these ice crystals will invariably strike the next snowflake behind or the next bit of the same snowflake deeper in and eventually reflect back. Since no one wavelength is preferentially absorbed or reflected, snow spots the color of the sunlight reflecting off it, which happens to be white.
Incidentally, snow is not always white.
Snow appears white only it has many air bubbles, allowing the light to reflect back in quick time. In most areas, the advent of summer results in the ice crystals melting into water, just like an ice cube melts when warm. Water is transparent. Light passes through water without any of it reflected or absorbed, and hence unlike snow, water has no color.
However, in the Polar Regions the situation is different. When the ice at the surface melts at summer, it reveals a new overlying ice layer that compress the remaining air bubbles. Now, any light that enters travels a longer distance within the ice before reflecting back. The light bounces around repeatedly between ice grains before reflecting back, and this gives the red end of the spectrum space enough time to be absorbed. The light that returns to the surface is blue and snow appears blue. Some regions of Greenland and other Arctic areas have Red and Green snow at times, because of this same principle.
A gradation of colors appears when poking a hole in clean, deep snow. Near the opening, the snow will appear yellowish. The ice crystals would transmit yellow and absorb other colors. As the depth increases, the color becomes yellowish-green, greenish-blue, and finally vivid blue, depending on the color absorbed and reflected back. If the hole is deep enough, all light is absorbed, and the color and light disappear completely.
The color of ice determines its strength and age. Arctic explorers and mountain climbers know that old, blue ice with fewer bubbles is safer and stronger than white ice.
Pollution can also influence the color of snow. When dust particles and other pollutants trap inside the ice crystals, the snowflakes thus formed tend to reflect black, with the dust absorbing all colors.