If I'm not mistaken, there's a way to import music; I saw a guide on importing models into the editor, and it seems music can be imported in a similar way. There's an option in the battle arena settings file to specify music.
Where exactly is this configured if you load an arena?
Added 2 minutes later
Alternatively, you can assign it to a hero (it will sometimes play during battles involving that hero).
Same question. It seems you can set music for a hero on the map: AdventureMusic.