More to explore:
Loom Knit - Cup/Mug Cozie pattern by Christina Fasoula via Ravelry.
Owl cup cozy This seems like it would be pretty easy to do this yourself! Just knit the main white strip and then knit the other parts, or make them out of felt with embroidery floss, and then sow them on.
Owl Cup Cozy | 10 Incredibly Cute DIY Projects Inspired By Animals
I really should learn how to knit...
loats of downloads for gift card holders, boxes, and this cup cozy
Ravelry: Cozy Loom-Knit Afghan pattern by Lion Brand Yarn
DIY Mug Cozies: I don't crochet/knit, so I hope one of my knitting friends sees this pin and makes me a set of these. ;)
Cozy Bear hooded Cowl Loom Knit pattern
Loom Knit Cup Cozy