Try using a fringe foot. I used mine to make fuzzy catipillars to applique on my kids things when they were young.

You might also look at couching different braids, make 3-D blocks, etc. Close your eyes when you are in the fabric store and forget all the "cotton" rules. Just make sure it is washable and won't come off if a little one chews on it (like some buttons and glue on jewels).