[Ardent]

I think the first speaker is an unnamed king of Cardolan.

When Merry is awakened by Tom Bombadil in the Barrow Downs he is wearing a gold circlet and says: “ The men of Carn Dum came on us at night, and we were worsted. Ah! The spear in my heart!”

The King of Carn Dum was the Witch King of Angmar, Ringwraith, Lord of the Nazgul. After defeating Arnor he sent wights to inhabit Cardolan, making it a place of terror. I would expect the second speaker to be him because:
1/ his origin was in the Second Age and Angmar only arose in the Third.
2/ Angmar was cold, dark and mountainous
3/ his fate was foretold by Glofindel upon the destruction of Angmar.
4/ wanting justice his victim would have him speared through the heart.

The Barrow Downs remained and the ghost of the dead king was still there with the wights when the Hobbits were rescued by Tom. He took the dead king's blade and gave it to Merry, who used it to stab the Witch King on the Pelennor Fields.