What would the makeup of the culture consist of classwise? Is everyone, including all the women, start as a barbarian? Are the the other classes compatable with such a culture? What would the other classes postions in the culture be? Is it a barbarian ruling class with a multitude of thralls(commoners) or does everybody have to pull their own weight? Does the barbarian class have the skills to care for himself or is he like the fighter and incapable of functioning outside of his narrow combat role?
Personally, I see the barbarian culture being mostly barbarians. Coming from the cold, dangerous wastelands and havign to raid and fight to survive, the other classes just don't have what it takes to protect the tribe. Most members of the tribe start out with a level of barbarian as the rough and tumble world is all they're trained in and division of labor isn't really well defined. They have Craft and Survival so they can fight, make their own items, and fend for themselves in a sustance manner, fishing and hunting.
After a level or two, they might multi-class. Cleric being a class suitable for a barbarian culture. They'll need the magic and cleric is a suitable marial build. Wizard is right out. Bard has it's place as the memory of the tribe and culture and perhaps what little magic they are comfortable with. Rogue might be helpful to some but it's low hit points and skills based on avoiding combat or fighting dirty might not be seen highly by such a combat culture where the tribe's survival means everybody fighting as hard as they can in an instant.
Many of the other classes such as commoner, expert, and even rogue would be left for the thralls, the lower classes. Thralls are either a lower cast, slaves from conquored people, or those who have failed in normal barbarian society. They preform much of the professions and agriculture needed. In a dangerous society that they live in, these are not important skills and are left for the lower classes. In the undeveloped wilderness, one only needs to make a weapon, hunt, and kill and all other things such as farmers, lawyers, etc are luxuries.
There would probably be some prestige classes such as Barbarian Leader that would fill in some other needed roles of the society.