Animating a static, commercial snowman

So you picked up a wire frame snowman at your local home improvement center and now that you've plugged it in, it glows nice and bright but it just stands there. And you want to make it interact a bit more with your viewers by adding some motion. It's not as hard as you might think, but it does involve a bit of DIY engineering, and often it turns out to be the one-of-a-kind-I-hope-I-never-have-to-do-this-again kind of engineering.