This conversation has me interested in what a real Conan the Barbarian class would be like. Maybe I'll homebrew one...
If only I could escape the name "Barbarian" due to its 5E connotations. But I really can't think of a good name to describe a Conan-esque character other than Barbarian tbh. Athlete? Warmonger? Soldier? Meh.
I learned a long time ago that trying to fit complex characters into D&D's neat little class structure is an exercise in frustration. Though at backgrounds in 5th edition and kits in 2nd did give players the opportunity to fine tune their characters to a certain degree. I don't think you can come up with a Conanesque class that wasn't severely unbalanced as it would be stepping on the toes of most other non spell casting classes.