TL;DR: I wrote a tutorial about rendering snow with shaders (with three.js + WebGL).
I was inspired to write this by OutsideOfSociety's excellent Christmas WebGL experiment, which in fact taught me how snow shaders could be built. The shader you can build with my tutorial is waaaay simpler for educational purposes, but if you want you can complicate it as much as you want, once you master the basics.
Hope you enjoy the tutorial and learn something from it! :-)
Also, please let me know if you find any error or something confusing, and I'll try to fix or reword it as soon as possible.