It is unknown how the past Aku's destruction affected his existence.
Similarly to his TV show, he is a white horse wearing a red cowboy hat and a light blue bandanda.
The Quick Draw McGraw Show
Quick Draw was himself a horse caricature that walked on two legs like a human (as did Baba Looey), and had "hands" that were hooves with thumbs and could hold objects such as guns. This did not stop the show's producers from depicting him riding into town on a realistic horse, or as seen in the show's opening credits, driving a stagecoach pulled by a whole team of realistic horses.