Snowflakes are not perfectly symmetric . The most common snowflakes are visually irregular, although near-perfect snowflakes may be more common in pictures because they are more visually appealing.
Please see some very high resolution photos : ftp://198.77.171.17/pub/High%20resolution%20TIFF%20Snow%20Images%20from%20webpage/
Snowflakes can come in many different forms, including columns, needles, and plates (with and without "dendrites" - the "arms" of some snowflakes). These different forms arise out of different temperatures and water saturation - among other conditions. Snowflakes form below about -10 C (14 F), solidifying around a frozen center droplet.
There are, broadly, two possible explanations for the symmetry of snowflakes. Firstly, there could be communication or information transfer between the arms, such that growth in each arm affects the growth in each other arm. Surface tension or phonons are among the ways that such communication could occur. The other explanation, which appears to be the prevalent view, is that the arms of a snowflake grow independently in an environment that is believed to be rapidly varying in temperature, humidity and other atmospheric conditions. This environment is believed to be relatively spatially homogeneous on the scale of a single flake, leading to the arms growing to a high level of visual similarity by responding in identical ways to identical conditions, much in the same way that unrelated trees respond to environmental changes by growing near-identical sets of tree rings. The difference in the environment in scales larger than a snowflake leads to the observed lack of correlation between the shapes of different snowflakes. The six-fold symmetry happens because of the basic hexagonal crystaline structure from which the snowflake grows. Surprisingly, the exact reason for the three-fold symmetry of triangular snowflakes is still a mystery.
http://en.wikipedia.org/wiki/Snow#Geometry
http://www.its.caltech.edu/~atomic/snowcrystals/faqs/faqs.htm