Yes. I installed mine in Jan of this year, in the middle of a Canadian winter. The player worked fine the whole time. I started it up in the morning and let it boot while I was warming up my car. I also started it up in the cold several times per day, all without a problem. The only real worry is condensation forming when you open the door. But, if your case has a good fan and your HD is fairly warm then it shouldn't be an issue.
I am from London, Ontario. Interstingly enough, my hard drive failed when I was in Cleveland in June for the 2000 DeLorean Auto Show. However, I attribute this failure to a drive manufacturing defect in the control board, as there was no indication of physical damage to the disc surface when it failed. That said, Cleveland may be a bad place for hard drives :-) By the way, Quantum replaced my drive on warrenty...
London, Ontario, Canada
Player: Cyrix 200, 32MB RAM, 10.2Gig Quantum HD, Onboard EtherNet/Sound/Video, Custom Lexan Case, Arise DC-DC, Win95 Kernal w/Custom Player
Car: '86 Mazda RX-7 w/Basic Performance Upgrades