According to the Early Ford V8 1938 1939 (restoration) Book, wind up clocks were standard on the 38 and 39 deluxe models. 1937 had both wind up and electric. You should be able to tell if yours is electric or windup as the windup only had an electrical connection to its light.
I have drained a battery by leaving the key on or not turning the radio completely off. Other possibillities are a stuck brake light switch, heater or turn signal left on etc. but these should become obvious when you recharge the battery.