I prefer to remove the battery and charge it the odd time during the winter. I also loosen the rad cap. I've seen my rad hose collapse come spring time. Loosening it stops that. A cover will keep the dust and dirt off the paint. Anytime you can keep that off is good when it comes time to clean the car in the spring. I know some people like to not have the doors completely closed so the door and glass rubber is not tightly compressed.
i do the same an crack the doors, hood an truck to take the pressure off the rubber seals. also i open the glove box so it's not a small closed up space for those little furry things. plus a good quality trickle charger. an i do place 4 mouse traps in the car an check them a couple times a month.
Fill the fuel tank (preferably with premium) and add fuel stabilizer. Be sure to run the vehicle to move fuel stabilizer into the carburetor, fuel rails, injectors, etc. The fuller the tank, the less room there will be for air, which carries moisture that can lead to fuel contamination and possibly rust within the tank.
Check the antifreeze/coolant.
Add air to the tires, preferably 5 lbs more helping stop flat spots.
Place baking soda refrigerator packages or Irish Spring Soap Bars in the interior and trunk areas.
To keep insects and vermin out of the car, put a plastic bag over the air cleaner/air inlet and exhaust pipe(s). You also can cover these with aluminum foil and tape securely. Place mothballs in an old sock around the outside of the car and insert steel wool in the tailpipe(s).
Take one of the following actions: Unhook the battery by removing the negative cable first and store it separately — never on a concrete floor and preferably where it will not freeze; or leave the battery in the car and put a battery tender on it, if there is power available. That way if you want to start it a few times in the winter you don’t have to put the battery in and out.