I've got zero knowledge in css and I literally don't know what you should change in the code but here's a theory on every falling objects which I think should be applied to the snow.
1. They all have an initial velocity
2. On every frame, add gravity which should be constant.
3. If snow touches the bottom of the screen, add friction and, reverse and reduce it's velocity
I have never tried this myself, and am usually annoyed with sites that use it, but your page seems more like art than content?
A quick web search brought me to this page...
maybe it will help your cause?