We often only turned on the water heater about 30 minutes before we needed it but that was in mild weather.
In extreme cold, down to -25F in our home location we kept the water heater on in electric mode because it kept the tank and lines near the tank from freezing. Even if your tank is gas use only, I'd run it on gas to better protect the unit.
We rented a residential size tank our local gas company would come refill to avoid taking the rig out when it was used up, which was indeed less than a week in extreme cold. In our area they would not come refill anything less than 200G though. Maybe in your area they will refill a smaller one.