Ubercart

I don't think anyone's really done this yet, so the short answer is that it's not possible. You might be able to work it through a custom checkout pane, or if you can alter your setup a little bit you might try UC Node Checkout. That won't add anything to the checkout form, but it lets customers create a node when they add a specific product to the cart. It ties the two together so you can find the data after the user has checked out on the node they created.