This is an old bug, but I think I shoud report it once again.
Every time I command my northern spearmen to use one handed weapons (key z, right?) they completely ignore me, they don't obey. If you give the same order to the unsullied, they'll use their short swords with no problem. (I haven't tested the dornish spearmen yet).
This seems strange to me. If you take a look in the northern spearmen inventory, you'll see he has a broadsword, which could be useful in siege. But doesn't matter how many commands you give, they will never obey your oeder to use one-handed weapons :'(
Hmm strange, I have checked both troops and I cannot see any difference between them that would cause issues.
I will leave this open incase you find issues with others too.
I've already tested the dornish troops and the veteran freerider and they work perfectly.
I imagine you problably had a hard work to make those northern spearman, but what if you remove them from the game and and add one spear to the northern guardsman and to his "evolution" (northern househould guard? I don't remember the name)? They also have good polearm skills.