Some additional lessons learned:
Wrapping a towel around your hands and securing them with velcro wire organizers is a good way to protect your fingers when grating carrots, but it's a terrible way to actually grate carrots. The carrots slip, the towel restricts your fingers, and the wire organizers don't always hold the towel in place. Instead, I have purchased these. They are rough gloves that can be used to scrub dirt off potatoes and carrots. I have found another use for them. They are great for protecting your hands while still getting the job done.
When adding the powdered sugar to the frosting, add in a couple of tablespoons at a time. I'm not sure if they really avoid curdling but the frosting came out perfect so I'm going to roll with it. Be careful - it can get messy. Powedered sugar flies.