given enough time the HDD will drop the ambient temperature of the car. Unless you introduce a heat source. Which may drain you battery.
There really isn't any kind of insulation that would keep it warm overnight (6-12 hours). Are you parking outside or in a garage?
From personal experience my HDD will work in a car that has been left out overnight in 5 Degree Fahrenheit weather. If it is much cooler out it take 5-10 minutes for the car to warm up then it runs fine. What temperatures are you experiencing? Many cold weather mp3car'ers will use solid state hard drives for booting as an alternative