Sorry about your inclement weather! I'm not sure about B. foliosa specifically, but many of my begonias are outside and come back from damage. I would get it in if you have the space, and probably wait a bit to cut it back more than the very obviously dead stuff. We have frosts and freezes, obviously, more than you do, and I try to cover things with frost blankets or old sheets or whatever when a frost threatens, but even then I may get a good bit of damage. It's amazing how well they come back----usually! Good luck!