Janko Gravner at UC Davis and David Griffeath at the University of Wisconsin-Madison
have modeled snowflake growth, as reported on [this web page][1]:
> 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.
<br />
![Snowflake][2]<br />
Paper, code, and movies on this modeling are available [here][3].
Here is a [1min17sec YouTube video][4] of growth simulations following this model;
and here is a [26sec, more colorful set of simulations][5].
<hr />
<b>Added</b>. Some added detail from the G-G papers:
> The building blocks for snowflakes are hexagonally arranged molecules of natural ice (*Ih*). Just how the elaborate designs emerge as water vapor freezes is still poorly understood....
The solidification process involves complex physical chemistry of diffusion limited aggregation and attachment kinetics....Our basic set-up features solidification Cellular Automata on the triangular lattice $\mathbb{T}$ (to reflect the arrangement of water molecules in ice crystals).
To echo Igor, it's "not so simple"!
<hr />
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][6], 2005.
Comparisons of the shape to "observed snowflakes" are made:
<br />
![Snowflake Observed][7]<br />
[1]: http://www.physorg.com/news119784799.html
[2]: https://people.csail.mit.edu/~orourke/MathOverflow/Snowflake.jpg
[3]: http://psoup.math.wisc.edu/Snowfakes.htm
[4]: http://www.youtube.com/watch?v=kEWYVCbOskQ
[5]: http://www.youtube.com/watch?v=N_a2oTC1Ekk&feature=endscreen&NR=1
[6]: http://journals.ametsoc.org/toc/atsc/62/5
[7]: https://people.csail.mit.edu/~orourke/MathOverflow/SnowflakeObserved.jpg