Could a Supreme Court Judge preside in the nude if he so wished?

Or any judge for that matter? Me and my friend were talking about how a court room isn’t technically a part of the US or anything but what the judge wants it to be, thus if a judge wants a gun in his courtroom he can have one.
Never mind the implications of the reasons of being nude, let’s just say that someone one day forgot his cloths, didn’t feel like going home, so he did the entire trail in the buff… could he?
I say yes because, like I mentioned the gun, it’s his world inside those walls and if his world states that one should not have cloths on, then so mote it be!