Simply copy to your plugins folder, go to Plugins and Activate it. That's it.
Plugin adds a new "Let It Snow" category to the left column of the Admin Panel instead of adding a config link inside Settings, but that's a minor complaint.
The snow (just large dots) flicker quite a bit, but this in more due to the nature of how such animated plugins work than any flaw in programming, and the "quality" of the snow can be tweaked in the settings.
My own blog has a white text window on a black background, so "white" snow would be a problem, but the plugin lets you set the color, allowing me to set gray (#aaa) snow that appears on both backgrounds just fine.
Quick & Easy way to add a snow effect to your blog.
(Update: Does not seem to work with IE. I'm a Firefox user and didn't notice before.)