DM's have authority over their games - Yes he can do that.
However... conjecture aside...
Vikings are regarded as some of the most successful barbarians - hence the Viking Age. Vikings utilized polearms. Yes... it's true. But they weren't called polearms of course.
Our friends from Hurstwic can provide some useful information.
The Atgeir: The atgeirr was Gunnar Hámundarson's preferred weapon in Brennu-Njáls saga and is usually translated as "halberd" (although sometimes as "bill" or "javelin").
The Flein: Usually translated as "pike". The weapon is also called a heftisax, a word not otherwise known in the saga literature. The saga says that the weapon had a wooden shaft and was equally suited for striking or stabbing.
Another good resource would be Wikipedia. Of course everyone uses wikipedia. The important thing for your DM to consider is different cultures. A halberd doesn't have to be called a halberd. Different cultures called the same weapon different things. Also, barbarians are simply any culture that isn't "civilized."
The Roman Empire typically referred to anyone not Roman as barbarians. Not all barbarians are created equal. The Mongols were barbarians, but fought on horseback with bows and arrows. Most Germanic tribes fought with longspears. The Old Germanic word for Spear was GerGer and many historians attribute Ger + Man = Spearman. Germania = Land of the Spearmen.