I'm all for exotic swords and armor. Japanese, Chinese, and Middle Eastern swords come to mind.
And a barbarian might as well rush into combat with a couple of animal hides stitched together, foregoing protection in favor of mobility.
But Conan is a little much. As much as I've loved the movies when I was a kid, I don't think it prudent to go into a swordfight in your underwear.
I could go with a class or kit that is specially trained to fight very effectively with no armor, but would still suffer heavy penalties.
Well then you certainly should check out some older cultures like German tribes, Gauls, even Celts... Some of them were running into battle naked...
I am not saying that majority was doing that, but some were. The idea of an almost naked barbarian is not that far fetched as you may think.
There are accounts of celts going into battle naked around 4th-5th century bc , so as not to hamper their mobility, and to intimidate their opponents. Conan really was a rather conservative barbarian in this regard.