It's really all about how much moisture is in the air where the flakes grow. With that said, typically the colder the air, the less moisture it can hold, so when you have very cold air, the air is also very dry and you do not get big flakes to occur.
The temperature range where the flakes get largest is not so dependent on actual surface temps as it is where the flakes are forming, but in general, when it gets colder than around 10 above, it's hard to get big flakes to fall.
-John