How about Evernote? I haven't tried especially TextEdit files with it, but whenever I need some text (pictures etc) on the road, that's what I usually end up using. Write the documents on the iPad or the Mac, then when home or on the road, use the other devices to continue editing them, and if later needed on something else, just export it where needed.
I use Notes for simple text stuff. I don't have some compelling need for text files on my iPad, I'm just wondering out loud why Apple bothered to make desktop TextEdit aware of iCloud without providing a way to use the files away from the desktop.