Well, let's think about this and consider Fantasy's most famous Barbarian (Conan, of course).
The first definition of "Barbarian" was "foreigner who doesn't speak Greek". To be strictly accurate, this was ANCIENT Greek, so it could refer to any culture from the Romans, to the Celts, to the Scythians, to the Persians. Conan was Cimmerian (a tribal culture that looks rather like the Celts).
So, IMHO, Barbarians should, by definition, be foreigners. They would have problems with accents and etiquette and lack some "civilised" skills. OTOH, they should have skills/abilities that are unusual in the "host culture". This could be anything; the Barbarian might be the Ranger, the mercenary/military specialist (or even the Warlock). They don't have to be clones of Arnold Schwarzenegger.
TLDR. The Barbarian is a role-playing tool and needs to be designed as part of the world-building. The Barbarian is something that the locals would see as very foreign