Elmer's Glue on Canvas, then paint the whole thing. I have totally done this, but with a hot glue gun. Elmer's Glue seems to be a better idea since hot glue leaves behind strings and is harder to work with.
Snowman painting that I think I could use for inspiration to create a card or craft project for the kids. I think using ribbon for scarf and maybe foam for the nose and maybe even felt for the hat would be cute.