Snowflakes Falling is the an original song by Jon Cheney. The song was originally conceived with lyrics, with the first words being “Snowflakes falling,” as you can easily hear in the melody. There are a lot of other lyrics that may be shared at a later date, but for now I will leave it to your imagination to make up the rest.
This song is also available in the full piano book for "Softly Christmas" available here.