Let me start off with some facts concerning lore, as I prefer to always do.
First off, I'm not sure what to think of "The war just started" and already moving to Northrend, Northrend was barely explored or attacked by the races of the Alliance, only the expedition of Arthas Menethil had been there since the start of the Plague Wars, the elves did not follow persuit until after the destruction of the Sunwell, already a time into the war. Preparing for the assault on Northrend was not done within the day, which brings me to another point: It takes days to travel by boat from Azeroth to Northrend, not hours.
Granted: Zeppelins are faster than boats, but I do doubt they would decrease the travel time by that much, especially since the Goblin zeppelins are scrap-builds made in an era where ships dominate the seas.
Also, elves value good warriors, and would not be as incompetant to send fresh warriors against an enemy that can turn their corpses into stronger zombies.
Moving on, the Lich King, at the time of the elven attacks on Northrend, was still a frozen piece of armour in ice, death knight Arthas at the time had not yet taken the armour for himself and only held Frostmourne. Also, Arthas was at the time still in the capital of Lordaeron, Lordaeron. The elven attacks had forced him to retreat to Northrend to save the Lich King.
Upon arrival Arthas avoided as much of the elves as possible, and to my memory never did willingly bring the fight to them which is also why the Nerubians had brought him to Azjol-Nerub, to avoid conflict and to win time.
By the time that Arthas freed Ner'zhul from the ice and took his armour the elves were already packing their bags and fled for Quel'thalas and Outland, no elf would still be arriving to face Arthas. The latter is a conclusion drawn from the final cinematic of Warcraft III - The Frozen Throne, in which Arthas takes the helmet and seizes it as his own, as he puts it on he sits down upon the throne, no sign of battle is seen in all of the Northrend wastes.
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On a smaller note: It seems illogical for the Lich King to, if circumstances are right, take an untrained body with little potential to meet the eye, and to raise it to become an instrument of fear and destruction.
I'm afraid I have to turn this application down for now, the lore of Death Knights is understandably difficult, especially to those that haven't done Warcraft III or paid close attention to it's dialogues, but it has to be correct, or in the end we'd all be claiming the opposite things.
For roleplaying help feel free to ask.
