Don't prune until the last danger of frost has passed and you can get a better idea what is damaged and what is healthy. You can check by making a small incision in the bark of the plant. The layer just below the outer bark is the cambium. Dead tissue will be dark. Healthy tissue will be green or a lighter color than the dead material. By early spring, some new buds might appear, which will show healthy tissue. Remove all dead tissue at this point.
Don't forget to keep watering regularly until then. It's not true that you don't have to worry about water during cold temperatures.