Safely store items in Gerdur’s house

See Equipment AI bug (bows).

Experiment with different bows and arrows. I can get Jenassa to use a Glass bow and Glass arrows. If she runs out of arrows she reverts to her standard bow. Since I rarely have enough Glass arrows for her, I give her a large stack of Iron arrows.

Also keep in mind that the follower is oblivious to your Smithing upgrades. The follower only looks at the base damage of the equipment to decide which is better.

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.