Cocytus

From the Soulcalibur Wiki

An ancient sword dug up out of the permafrost. It is always cold and causes freezing burns in those it wounds. Because of its low temperature, droplets of water appear on its surface and fall to the ground like tears, giving it the additional name of the Crying Sword. As one would expect from its cold temperament, it is unaffected by the state of its wielder's heart.