And I mean surround it with a gap-less wall of moth balls in a ring of defense against unauthorized intrusion. The mice don't like it to cross this line in the sand. This can be augmented with some traps. But keep in mind that traps work my attracting the mice not scaring them away. However, I think that would do better at keeping dust out then mice.
Mice like to chew through things like that and hide inside.
If they get inside you'll never see them or their droppings. This brings us to the topic of periodic inspection. Every 2 weeks or so, it's probably a good idea to take a look at the car. I'm of the school which says don't start the car during the storage. The reasons are starting it puts lots of thermal stress on the parts which are all probably sitting around 30 to 40 degrees.