For intents and purposes, container plants have their roots exposed to the elements.
Sure they're encased by a container but unlike growing plants in the ground the container can freeze thereby doing the same to your plant roots.
So you see, we are more worried about the roots of the plant than we are the branches and leaves. OK, so now what.
A great insulator are the Sunday funnies. Newspaper! Though not very aesthetic wrap several layers of newspapers around a plants container. Even overlap it at the top and fold over.
If it's a decorative container you're working with, protect it from the newsprint by covering with a trash bag first.