I haven't tried over-wintering but I would cut back the one with the dead top because the dead leaves won't come back. You'll then be able to more easily see if it starts to regrow. I'd leave the one with living leaves for now, at least they give you something to monitor its condition with, and they can always be cut back later if there's a reason to whereas they can't be stuck back on
Important thing is to get them in before the next frost.
