It's a 2002 Z06 Vette. Part of my American dream! I've lived here for 2 years now and so far no evidence of mice in the garage. I'd say it probably stays about 10 degrees warmer in there than the outside temps, or at least it feels that way to me. I hadn't thought about the lack of heat keeping mice out, but that sure does bring me some peace of mind.
Mice are not hampered by a lack of heat. If they feel comfortable/safe in there they will get in there. Seen to many cars that sat in unheated structures with mice damage.