Here's my checklist each winter:
1. Verify with a tester that the coolant is protected from freezing to about -20.
2. Remove battery, give it a full charge and store in basement.
3. Add fuel stabilizer to tank.
4. Place jack stands under frame. (unloads suspension and keeps tires from flat spotting)
5. Place sticky traps all around cowl vent to keep mice from going into heating ducts. (also put some inside on floorboards)
6. I don't cover it, I let the dust build up on it and don't let anyone touch it.
At least once a month I open the doors and hatch and let it air out, then install the battery, start it up and run in gear (since it's off the ground) until it reaches operating temp. This gets all the fluids moving in the tranny and differential. I pump the brakes and operate the parking brake, turn signals, 4 ways, heater, wipers, power windows/locks and honk the horn once.
I may go overboard, but I own 9 vehicles and half of them get stored, so this is a full time job for me during the winter.