Read/Edit Textedit icloud files on an iPad
As @patrix said there is no way.

However you can use iA Writer. It's an application available for Mac, iPad and iPhone, which allows you to read and write txt files, which are the same produced by Textedit. It as a native iCloud and Dropbox support.

Unfortunately it is not free.

Alternatively Brett Terpstra has an amazingly comprehensive review of iOS editors where you can find a replacement or be alerted when a program does in fact cooperate with TextEdit for document storage in iCloud.