Put down a deposit on a car sold by a private owner, called the next day to cancel the sale, owner cashed the check for the deposit (deposit for Mustang) written on the check, owner would not return deposit. Is he legally bound to return my deposit.

Looks like you might be out of luck, unless you have a written contract that says otherwise.

Source: Be Careful When Leaving A Vehicle Deposit | There Is No Automatic Right To A Refund - Consumer Reports News

He is not legally bound. A deposit shows good faith that you want that car. When you give someone a deposit, you are saying you want it and they should stop advertising it and tell anyone else that is interested that it is no longer for sale.

THAT is the whole point of a deposit. What good is it if people give money to hold something and it really doesn't mean anything?

You would have to go to small claims court over that one and I doubt you could have any chance of winning.