Are you heating the garage so that you can work in there, or are you heating it so that your car does not go rusty? If it is the latter, then a de-humidifier will be a lot cheaper to run and be just as effective in preventing rust. According to the people who store long term vintage cars, 55% relative humidity is the optimum point for relatively little rust damage and good conditions for wood/leather etc. Remember that the worst condition is to drive a cold car into a warm garage: moisture then condenses on all the metal.
As far as mice are concerned, I have surprised myself by finding an electronic unit that actually appears to work. It is called a Pest Stop 2010: I have it set to "random". 20 feet away is a stable yard that has a lot of mice problems, so I can't work out if the unit works, or if they just prefer the food in the stable yard!
Oliver S.