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 />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
![Snowflake][2]<br />
Paper, code, and movies on this modeling are available [here][3].
<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][4], 2005.
Comparisons of the shape to "observed snowflakes" are made:
<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
![Snowflake Observed][5]<br />


  [1]: http://www.physorg.com/news119784799.html
  [2]: http://people.csail.mit.edu/~orourke/MathOverflow/Snowflake.jpg
  [3]: http://psoup.math.wisc.edu/Snowfakes.htm
  [4]: http://journals.ametsoc.org/toc/atsc/62/5
  [5]: http://people.csail.mit.edu/~orourke/MathOverflow/SnowflakeObserved.jpg