Does being targeted with Moonlight Hunt allow my creature to return damage?
No.

The only thing that Moonlight Hunt does is specifically what it says: each wolf or werewolf that your opponent controls will deal damage to your It That Rides as One. Your creature will not deal damage in return because the spell doesn't say it does.

Note that Moonlight Hunt does not cause creatures to fight each other. "Fight" is a keyword that causes creatures to deal damage to each other; which may be what you are thinking of. But Moonlight Hunt doesn't use the word "fight"; so it doesn't have anything to do with "fighting".