[DesktopSnow] (freeware) will allow you to add snowflakes (and other images) to your desktop. The flakes show up over top of other Windows unless a Window has it's own "Always On Top" option set. It has several other images that can be used. Things like Tennis Balls, Stars, Yellow Flowers, Leaves, etc.
Like the other program, if you have a program that has it's "Always On Top" setting to yes, then the flakes will be behind that program. I have a feeling that you'll run into that problem with most "snow flake" programs.
Also be suspicious as these are the types of programs that malware/adware/scammers target and try to get people to install so they can install their own hidden software along with it. I've checked these two and feel they are safe.
Maybe someone else can give you a better option if one exists.