I don't understand how they are even close to symmetric. The 'seed' seems unlikely to be symmetric. There is no way for one 'arm' to communicate directly with another. And the conditions (temperature etc) is unlikely to be completely uniform around that seed.
> The ice crystals that make up snowflakes are symmetrical (or patterned) because they reflect the internal order of the crystal’s water molecules as they arrange themselves in predetermined spaces (known as “crystallization”) to form a six-sided snowflake.