This program is called "DesktopSnowOK". It is a tiny tool which can add soft, fluttering snowflakes to your desktop in a click. Despite being only a 78KB executable, DesktopSnowOK is highly configurable. There are twelve flake styles to choose from, for instance, covering everything from tiny orbs to chunky full-sized flakes.
And a host of other options (soccer balls, base balls, tennis balls and more) ensure the program will be useful - if that word really applies here - all year long. You can also choose the number of flakes you'd like on screen at any one time, their transparency, and how quickly they should fall.