You know how they say no two snowflakes are alike?
It turns out that they're so sensitive to the conditions they form in, and are also fragile in a turbulent area, that the odds of two snowflakes growing in precisely the same way and having the exact same collisions breaking pieces off as they go are pretty small.
There are, however, a few main shapes of snowflakes that all snowflakes follow.
A researcher at CalTech has developed a way to grow perfect snowflakes of the various types, and in addition to doing science on how the crystals change their growth patterns with different temperature and humidity conditions, takes absolutely gorgeous pictures of his snowflakes as well as "wild" snowflakes.
Don't ask me how many hours I've lost there, or whether distilled water has mysteriously appeared on my grocery list...
Chemically, every one of those snowflakes is just water ice. If you look through the photo gallery, you can see that even though they're all different, they're also all hexagons, with the lines on all of the features matching a hexagonal pattern.
Using a compass and a straightedge, you can draw as complex a snowflake as you have patience for. With a bunch of concentric circles, the fact that the edge length of each side of a hexagon is the same as the radius of the circle its corners touch, and straight lines parallel to the line through the centre, you could make something like this (relatively simple) snowflake:
Artificial snow of the other sort, the kind that covers ski hills when not enough natural snow falls, is very different stuff, despite being also made of water ice. It's made by spraying a fine mist of cold water into the outlet of a high-velocity air stream, which tears the droplets apart even more. The air is below freezing, and between evaporative cooling due to the airflow and simple heat transfer to the freezing air, the tiny droplets freeze solid and fall as something similar to snow. It actually looks like little blobs, instead of little hexagonal branches:
It's not as good to ski on as the real stuff according to some, but I'm not such a skilled skier that I can really tell the difference. It covers the rocks. I'm going skiing.