Not the same car, but I have owned my 1933 Chevrolet for 42 years and here is what I have always done to store this car, and my other collectable cars for a matter of fact, here in southern PA.
I fill the gas tank, then I drive them into the garage, turn the car off, remove the key and leave it sit until it is time to start them in the spring. In the spring I put the key in, start the engine and drive them.
With the mileage I put on the cars, I change the oil once every two years in the fall. I have never had an issue.
For the 1933 Chevrolet and Triumph TR4 there is nothing to drain the battery so the battery still has a charge after sitting for 3 months.
The only exception is my 1984 BMW 633 CSi that has an electric clock that would drain the battery, so I use a Battery Tender brand charger to keep the battery topped off, but the other option would be to just disconnect the battery ground for the winter.
Bob Beers
1933 Chevrolet
1962 Triumph TR4
1984 BMW 633 CSi