If you wish to put some falling snow on your webpage, all you need to do is go to this site:http://www.hscripts.com/scripts/JavaScript/image-fall.php
The falling image they use is a leaf, you just need to create your own snowflake image and replace it and you have your own snowfall on your site. Make sure you do not remove the copyright information from the code.
If you want to add this to your SharePoint site, simply put the javacript file in your document folder along with the image, and then copy the url of the image into your javascript code file. Then create a content editor webpart and copy the supplied code that refers to the javascript file into the source editor (making sure that you change the link to point to the document library where you have put the javascript code file) .