Since it seems that's the direction we're going, that Frostmourne victims may have split souls.
We have the quote
"Whomsoever takes up this blade shall wield power eternal. Just as the blade rends flesh, so must power scar the spirit."
Which for me not fully justifies this split soul, but at least it's there in some way that it can scar the soul.
So, as the first "victim" of the sword, I'd image it also true for Arthas. What do you think?