Not directly. In fact, cold batteries are supposed to keep their charge better than hot ones. But that's only when you don't use them.
When you use them, the chemical reaction, which releases the electrons in the battery, goes slower so less current is available for the starter motor. In addition to this, the oil in the engine is thicker when cold, so it's harder to turn the engine over. And fuel evaporates slower which, combined with less than perfect starting technique, causes more difficult starts. To the point that people drain the battery easier.
So yes, you'll find more flat batteries all over the country when cold. Just this morning I had to get external power to start - battery didn't have enough juice left to pull the engine through its first compression.
[Cue discussion about correct priming and starting techniques]