I always sort of assumed that when Arthas shattered the Frozen Throne and donned the Helm, he took some elements of the Plate of the Damned and added it to his own armor - since the armor that Death Knight Arthas wears and the armor of the Lich King version of Arthas is subtly different, with additional flourishes and such. Part of the issue with all this is that between WC3, various artist illustrations, WoW/WotLK, and again in WC3R the visualization of Arthas' armor as a Death Knight and even as the Lich King is a bit inconsistent at best.