This used to be bundled with Jetpacks modules and I believe you can only access it now if your site is hosted on the main WordPress.com, but never fear you can add it to your site with a small snippet of code.
First download the latest version and move snowstorm.js in you js folder in your theme, there is also a minified version that you can use, but you may wish to change a few variables in the script.
Then in your functions.php add in the snippet below (minus the opening php block)
The author of the script has allowed some of the variables to be changed.
That’s it you now should have snow falling all around.