Certified GKH Gardening Expert
Butterfly bushes are generally hardy to zone 5 or 6, so unless yours is in a container, it should do fine outside. I would mulch it well, though. If you expect extreme temperatures, you could cover it.
In late winter, or early spring, cut it down to 6 or 8 inches. They grow fast and bloom on new wood, so there is no reason to keep the old growth. (If your bush is in a container I would bring it inside to an unheated garage or basement.) I have found most of the butterfly bushes I've owned were short lived. They came back only two or three years. However, I had one that returned more than 10 years, so you never know.