Ooh, I can answer this, though I am no longer a New Englander and not a math person by any chance. (; Snowflakes (or snow crystals) actually are often identical at very high altitudes, I believe, but develop their patterns as they fall and are influenced by their environment.
You might want to look up the work of Wilson A. Bentley, or "Snowflake" Bentley... he is my #1 hero and I have a minor obsession with him (wrote a series of poems about him and am very slowly writing a biographical novel). He was a farmer from Vermont who developed a method for photographing snow crystals. They're absolutely gorgeous.