While the death of Winry's parents is a significant plot point, the person responsible is never explicitly revealed, and Winry's character arc focuses on her grief, her desire to become a skilled mechanic, and her relationship with the Elric brothers.
It's important to note that the details of Winry's parents' death and the identity of the killer are left open to interpretation, adding to the complex themes of war, loss, and revenge in the story.