During the Dance of the Dragons, Shrykos, a young she-dragon, was bound to Prince Jaehaerys Targaryen.
An angry crowd broke into the Dragonpit and killed Shrykos. The crowd was half-crazed and angry because a prophet with only one hand, the Shepherd, started ranting against all dragons. Shrykos was slain by a woodsman named Hobb the Hewer who leapt onto her neck and drove his axe into her skull as she screamed and turned to try to get him off.
When Hobb hit the dragon seven times with his axe, he roared out the name of each of the Seven. His legs were locked around the dragon’s neck. The Stranger’s blow was the one that killed the dragon; his axe crashed through scale and bones and into Shrykos’s brain.
Shrykos killed a lot of people in the Dragonpit before he was slain; there is no doubt about that. Shrykos was never on a horse.