I guess I put that a bit awkwardly.
When you get to clean the stalls, at some point your character decides to undress because she is so hot after that exhausting work. You don't have a choice to NOT do it.
So, no matter what armour you wore when you started the quest, for the moment she will take it off.
She'll just not put it back on again (automatically) after the quest is finished.
You'll have to put it back on in your wardrobe.