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I don't do anything but fill up the gas tank. I store my 65 Mustang from about the first snowfall in early November until the Spring thaw in late March (about 5 1/2 months) and it starts right up with no problem. I did the same with a 29 Ford street rod until I sold it last year. I think keeping the gas tank full probably keeps condensation to a minimum. It would not hurt to put a gas stabilizer in the tank, but I've never used it. Be sure you have the proper amount of anti-freeze in it for your area. It's 31 below zero here this morning and probably near that in my unheated garage...
I don't drive mine in winter so I took a few steps:
Check for leaks, check fluid levels
-Bring Antifreeze down to -40F (yes, it actually does get that cold atleast one night every winter).
-Wash it, dry it, wax it
-Take it for a highway drive
-Park it in the shop
Every time the weather is near 0 or a little warmer I like to:
-Start it and run it untill the t-stats are open for a while
-Pump brakes to keep cylinders from sticking
-Check oil, antifreeze, smell the gas
If it is nice and clear out I will back it out and wipe the dust off with a Cali-Car Duster.. for not moving and getting constant attention, they can get pretty dusty.
It would probably survive winter without all that attention, but when it comes to spending money on it, I would rather pay to improve it instead of re-repair it.
As long as the antifreeze mixture is sufficiently strong and the fuel tank is full of fresh push water, I've never worried much about storing a vehicle indoors for the winter. I've always been way more concerned about mice - my storage building is in the middle of a vast sea of farm land. Traps and poison don't do any good. By that time, the damage is usually already done. Mothballs are only marginally effective and stink the inside of the car or truck up. Cats are usually a sure thing but the maintenance is high and they have a nasty habit of climbing all over the cars. I finally resorted to buying an ultrasonic pest repeller and it seems to work pretty well.
What to do with the battery - depends on several factors for me. If I'm not running the truck on a regular basis thru the winter, I'll probably pull it and keep it in the house. I had a battery burst last winter in the camper. It had water added to the acid once too often and during a deep freeze it came apart at the seams.
Generally I don't do anything with them. Activating the battery by starting and charging seems to help keep them alive. We've seen -32 F and none of our vihicles suffered any problems during a week of that weather.
Fill the gas tank and add a shot of fuel stabilizer. Start it once a month and run till it reaches operating temperature.