Beethoven wasn't born deaf. He had progressive hearing loss over nearly 2 decades. Moonlight Sonata was written while he was still hearing quite well.

He did indeed continue composing after going completely deaf. While this is impressive, you have to understand that music is simply a language with rules (especially at the time he was writing, even though he was a rule-breaker). If you were to go deaf tomorrow would you no longer be able to write sentences? You know how grammar works and how sentences are formed. You even know how the words sound in your mind. Once someone knows the musical language as well as Beethoven, deafness, though a horrible thing which would prevent him from hearing the subtlety of actual music, would not stop him from writing it and even hearing what he was writing in his own mind.