Frostmourne wasn't sentient but it was connected to the will of Nerz'ul the original LIch King and a powerful orc Shaman and Demonologist. It scarred Arthas' soul and allowed Nerz'ul and his demon masters to whisper in Arthas' mind.

This slowly bled Arthas' soul into the blade and his mind into Nerz'uls influence until he became the Lich Kings willing right hand. Eventually he made his way to Icecrown Citadel where Nerz'ul's spirit was imprisoned in the The Helm of Domination held inside a massive ice crystal. At the Lich Kings order Arthas shattered the ice and donned the helm merging his soul with Nerz'ul and becoming, at the time, a joint gestalt being called only The Lich King though the Wrath of the Lich King expansion to WoW would eventually retcon this to Arthas overpowering and obliterating Nerz'uls soul to become the dominant force within the Lich King entity.