So, I was interested in seeing if I could get Iona to wear some more common clothes around the house. I pretty much just leave her there most of the time anyway, so there’s no point in her being always dressed for battle.
I couldn’t seem to get her to un-equip her standard armor, and she wouldn’t put on regular clothing or lesser armor while it was equipped. So, after I finished leveling and perking up my pickpocketing, I stole the Steel Armor straight off her back. After that, I gave her some more suitable house attire (via “Follow me…” -> “I need to trade…”) which she gladly put on. However, when I later left and returned to the house, I found her wandering around in her undergarments!
I checked her inventory, and found the clothes I’d given her were still there and her armor wasn’t. So, she had no good reason not to be dressed in what had been handed to her. Later, I figured out this continues to happen even if I leave a full set of Legendary-quality Dragonscale Armor with her.
And, later on… I found out this is also the case with Lydia and Jordis. They’ll all wear their clothes immediately after being given them. But if I leave them at home, I’ll return to find them bare.
Is this a known bug? Is there any way around it without using the PC-only console?
From what I’ve heard and experienced, your followers are predetermined to wear a specific kind of armor. For example, if I give Lydia light armor, she won’t wear it, even if she has nothing else equipped because she is preset for heavy armor only.
I did experience a similar issue with Lydia, though minus the nudity. I tried to give her a light armor helm. I would see her wearing it right after I equipped her with it, but after a couple of fights, it was gone. The item was still in her inventory but she simply refused to wear it. I believe this is because the light helm does not meet her armor requirements. In your case, regular clothing would not fit your housecarls preset armor specifications so they are simply unable to keep these items equipped.
That said, I don’t think there’s anything you can do short of using the console to force her to wear it.