Janko Gravner at UC Davis and David Griffeath at the University of Wisconsin-Madison have modeled snowflake growth, as reported on this web page:
the researchers were able to recreate a wide range of natural snowflake shapes. Rather than trying to model every water molecule, it divides the space into three-dimensional chunks one micrometer across. The program takes about 24 hours to produce one "snowfake" on a modern desktop computer.
Snowflake http://people.csail.mit.edu/%7Eorourke/MathOverflow/Snowflake.jpg
Paper, code, and movies on this modeling are available here.
A more physically based, 3D model is explored in the paper "Monte Carlo Simulation of the Formation of Snowflakes," by Maruyman and Fujiyoshi Journal of the Atmospheric Sciences, 2005. Comparisons of the shape to "observed snowflakes" are made.