Snowflakes are crystals, which grow based on the original frozen molecule. At the original freezing point, a six sided prism, with hexagonal top and bottom. is formed, and then as the crystal grows it warms and freezes to grow branches off each face of the prism.
During the crystallization process, the water molecules align themselves to maximize attractive forces and minimize repulsive ones. As a result, the water molecules arrange themselves in predetermined spaces and in a specific arrangement.
This process is much like tiling a floor in accordance with a specific pattern: once the pattern is chosen and the first tiles are placed, then all the other tiles must go in predetermined spaces in order to maintain the pattern of symmetry. Water molecules simply arrange themselves to fit the spaces and maintain symmetry; in this way, the different arms of the snowflake are formed.