The subject of a sentence is a word, phrase, or an entire clause that is showing us who is performing a particular action. In the case above, the noun clause <em>Whether we win or lose </em>acts as the subject of the sentence. You can replace the entire sentence with a single word; for example, the pronoun SHE: She is not important... Therefore, it will be easier for you to determine that it is actually the subject.
I began to read a book. It was really cool. I think it was called ‘The mysterious Benedict Society‘ (you should read it!) it was a book full of adventures! I mean the good and bad guys were twins! Can you believe that?