If the defining factor for a barbarian is their brains or strength, or lack of culture, then they're simply a fighter with a particular physical attribute or background. But if it's supernatural, as many of the subtypes have been, they're a class that stands on its own, mixing ancient beliefs in the spirits into enhancing their abilities. They may shrug off arcane magic as unnatural even if their powers mimic such, believing the study of arts that don't come from the natural world or from the ancestors are likely brought to this world by demons to lure mortals to ruin.
Hence, I see them as more the ancient Celtic barbarians, oft depicted as wearing paint to mystically protect them in battle while fighting naked, or simply generic cultures drawing upon the spirits of their tribal animal or ancestors to imbue them with supernatural strength against enemies. Whereas Conan the "Barbarian" is a harder sell because in the books, he wears clothes of the region and armor, speaks several languages, and is "barbarian" in the ancient Greek/Roman sense of simply being someone who wasn't Greek/Roman and therefore less educated, not how I see the D&D barbarian. But, his "barbarian" supernatural nature perhaps draws from his freakish feats of strength and invoking Crom (who eventually intervenes to save him). Which, perhaps makes Conan a 10th level cleric...
Something like that.