Is the killer of Hussein a disbeliever?

Husayn ibn Ali (may Allah be pleased with them both) was killed during the reign of Yazid ibn Mu'awiyah. This was one of the grave evils perpetrated by Yazid. He began his rule with the killing of Husayn and concluded it with the Battle of al-Harrah. Consequently, people loathed him, and his life was not blessed.