The theme to Skyrim is identical to the theme of Morrowind, but with the chorus added on top.
Wrong. partially right, but mostly wrong.
Skyrim's theme is similar to morrowind's, yes, but only for the fourteen seconds after the first chorus and the twenty seconds before the second. And even that's different, since the feel of Skyrim's theme is nothing like morrowind.
Skyrim's theme is its own.
here's an example of the difference using a violin/piano cover: http://www.youtube.com/watch?v=cAnQQcIncq0&feature=related
On the same instruments, the two themes are nothing alike