My housecarls won't stay dressed!
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.
The Skyrim Nexus has a mod called "Advanced Follower Tweaks" (AFT) that will help you resolve this issue on the PC version. I wanted all of my Hearthfire houses protected by housecarls and stewards wearing more than their own standard default gear.
The AFT mod allows me to permanently remove all items (including their default armor/weapons) from my housecarls/stewards, and assign them a new default set of armor/weapons. For anyone playing on the PC, I would highly recommend trying out this mod.
My guess is that NPCs try to maximize their armour rating. An NPC with the perk that provides a 25% bonus when wearing all light armor might forego a heavy armor part and prefer to wear no part (or an inferior light armor part) in that place, because the bonus for the other armor parts is higher than the heavy part's rating.
Now, I can imagine that the algorithm for this simply undresses the NPC, then tries to maximize the armor rating. If the NPC has no clothes with a rating above zero in the inventory, this would result in the NPC staying in underwear.
Another question here indicates that NPCs may "reconsider" their clothing at certain times such as leaving or entering a house. If you give an NPC only clothing with no armor rating, that would result in the NPC undressing every time they cross the door.
One way to check this (I have not got that pickpocketing perk yet, so can't) would be to give the NPC clothes with a minimal armor rating, like robes.
Since the effect is a bit silly, I'd call this a bug, even though it's tempting to call it a feature. :-)
To reset their gear, ask what they have for sale and buy all the listed steel gear. Double check by exiting chat and re-ask what they have for sale. This should show her complete default gear. I initially asked her while she was my follower and dismissed her to send her home.