Just recently, I heard about a little boy whose only Christmas wish was for snow. Snow in its simplest form is just frozen precipitation. However, the different types of precipitation form under specific conditions. For example, sleet is just very cold rain that freezes into pellets when it reaches the ground. However, snow isn't frozen water, it's really frozen water vapor.
Snow crystals form by a process of sublimation.
That's where water vapor turns to ice without first turning into a liquid form. Usually, a speck of dust or other tiny floating particle is needed to start the process. Something as small as a bacteria can even act as the trigger for snowflake formation. As the dust floats through the atmosphere, ice crystals form on the particle and begin to build into a snowflake. Individual crystals connect to other crystals and ultimately form larger structures.