I would NOT put a tarp under a car in storage and hesitate to cover them with anything except the most breathable material possible and, even then, only when there's a danger of stuff falling on or scratching them.
In any northern climate unheated space, you'll get condensation. Leave any tools out there....they'll rust. I have bikes - you park a bike out there and come in on a warmer than the past day (one of those 32 degree days in early Feb) and there will be condensation on all the chrome and even drips.
This will happen even if you hang it from the ceiling. The best way to resolve this is ventilation....Throw in a ceiling fan or two and put all four tires on some 2x8 lumber squares. If you can, put a dehumidifier in the garage...Keep the air moving.
As for the mice, etc. - they're real bad news. I'd a) get one of those electronic rodent deterrent things (you'll see them in JC Whitney, etc.) - They give off an inaudible decible pulse that keeps em away. If you can stand it, get some moth balls and hang them in baggies off your firewall and exhaust. Mice hate em (you will need to add a nicer smell to the car in the spring.)
I was in your position for years. It also helps to get in the car and run / move it every 2-3 weeks. The mice won't next if they're bothered regularly.
Your situation bugged me so much, I built this
- radiant heat in the floors, ceiling fans, full bath, cable and beer fridge and a constant 65 degrees.
