I would not store it in near-freezing temperatures. The biggest danger would be condensation (assuming the temperature fluctuates) that might lead to moisture in the electronics. This could lead to rusting and dirty connections. Or worse, some accumulated moisture could then freeze, with the expanding water ripping apart some internal connections.
I'm pretty sure the Warnings section at the front of the manual will tell you what the safe storage/operating temperature range is.
A good rule of thumb is that you shouldn't store your gear somewhere long-term where you wouldn't want to stay long-term. That being said, though, cold is generally not nearly as bad for electronics as heat. Actually, most electronics work better in the cold. Condensation can be an issue if you take a piece of gear from a cold environment into a warm one and immediately turn it on. This is why it's a good practice to let things warm up to room temperature before firing them up.
Personally, I wouldn't be too concerned about storing something in a garage that occasionally gets cold, but it may be better to find something that's a bit more temperate. I live in Minnesota, and there are times when I'll leave my pedalboard in my trunk during the winter on very cold days. Of course stuff gets cold. I just let it warm up before turning it on. During the summer, though, I would probably bring my board in the office during the day rather than leave it in the car. Heat exposure is what degrades things like solder joints in the long run.
Don't put gear that you've just used immediately into a cold storage area. I recall a friend came from rehearsal, put his hot valve amp in a cold garage and the next morning it looked like someone had tipped a glass of water into it.
When travelling, always let your gear acclimatise in its case a while before taking it out, particularly after a hot drive, when you turn up to the studio let your guitar sit in it's case for half an hour (if you can) before taking it out. With electrical gear after usage is more important so a gradual warm/cooling down would be recommended. I hear hot valves can even break during a bumpy drive home but I've yet to experience it.
Also, a gig bag for your POD may offer some protection. I use a Gator GK-2110 and it fits perfectly.