Snow forms when atmospheric water vapor freezes onto a pollen or dust particle, which creates an ice crystal. As it falls, more water vapor freezes onto the ice crystal to create snowflakes.
Mother Nature Network outlines the formation of snow in the following steps. First, snow forms when there is atmospheric lift, which means that warm, moist air gets stuck above colder air. This happens especially readily above lakes and other large bodies of water when temperature instability occurs because cold air collides with the warmer water vapor. Second, once atmospheric lift occurs, the water vapor condenses onto pollen and dust particles that are also in the air. Third, once it condenses onto the particles, the cold temperatures cause it to freeze. Finally, these frozen particles attract even more water vapor, which crystallize and eventually form snowflakes.
Although snowflakes are infinitesimal, they have symmetrical shapes because that is the way water molecules are organized. Each snowflake has six sides or arms. The shape, though, depends largely on the temperature at which the snowflake was formed. The National Oceanic and Atmospheric Administration points out that the colder the temperature, the flatter the snowflake. Warmer temperatures tend to produce long needle-like snowflakes.