I got home from a trip tonight, and when I arrived at my house, I got out of the car, and apparently my iPhone fell from my pocket onto the curb into a pile of leaves. I did not notice this, and proceeded to unload and go into the house. It was 10 degrees F when the phone was dropped. About 45 minutes later, I went to take the trash out, and heard one of the alarms i had set on my iPhone going off. I followed the noise and realized my iPhone had been sitting in a pile of leaves since I had been home! I picked it up, it has no water damage or anything, but the battery was barely alive. I recall it being in the 80% range before I dropped it. It was at 18% when I found it.
So yes, cold does a number on your battery. It's 6 right now. I'm going to crawl in a warm bed now.