Bougainvillea plants can actually take and tolerate the cold. But they'll even get damaged if it's really too cold. You can still take good care of such plants. In freezing temperature it would be good if you cover your plant with some old bed sheet. If you see any damaged part in your plants PLEASE DO NOT remove or cut it off. Wait for the temperature to get better. If you want some more information, then you must go through the link below:
ag.arizona.edu
ag.arizona.edu