In general, DnD has always had that clothing isnt considered armor, at some points things like light armor normally made of regular metal that would be considered light armor, would be considered unarmored for things such as spell casting if it was made of a supernatural light metal like mithril.
But I wouldnt say you were running around in your undies for no reason, clothes weight 1.8 pounds, and thats a lot of coins or jewelry.
