I have a 2007 legacy 2.5i, I dont have the same problem but close. As soon as it started to get cold out my cars radio would lose the presets and spit the cd out when you started the car in the morning after it sat in the cold all night, and then sometimes when you started the car the radio would just come on quick and turn back off but also lose the presets and spit the cd out. I noticed the car turns over harder but I figured it is just because it is colder. I cleaned the corrosion off from the battery posts and wires and put a little vaseline on the posts but the problem still happens. I was just wondering if maybe my cars issue is caused by the same thing causeing the radio/hvac issue.