Dean - The ones in these pictures are no longer mine; I sold them to these people, last year. I don't know what their plans for overwintering are. I would assume that they are going to do it outdoors. I think he told me that, last winter, he didn't do anything to them; no mulch, or covering, or anything. (I know our botanical garden has one mat that they don't bother to protect, and it comes back reliably.)
Personally, I'm going to do mine outdoors. I did one, in the ground, this past winter and, even though I accidentally broke it off, it came back quite well. Here's a link to a thread that I posted, when I uncovered:Uncovering the basjoos.
I will do one thing differently, with the potted ones, this year. In an attempt to save the p-stems, I had laid the containers on their sides. When I uncovered, all the stems were firm, and all had shoots, near the base. (see picture in link) When I cut the stems, about 3 inches from the top, they were green, in the center. I thought they would resume growing from that point (as the one in the ground did), but the green middle part pushed out only a quarter to a half inch, and then stopped. The shoots, at the bottom, grew rapidly though. So, this year, I think I'll leave the containers upright, and stuff leaves, etc. between and around them, like the one in the ground.