"Horsey" gets transformed by Adora into who is soon be known as "Swift Wind."
She-Ra transformed a lizard accidentally while trying heal
Animal Transformation is one of the many abilities given to one who controls the Sword of Protection (She-Ra, currently Adora). This ability is used to make any animal transform, physically changing them in appearance as well as giving them supernatural abilities. The energy to do so comes from the Runestone and the sword it is embedded in. The animal Adora transformed accidentally was a horse, which then became intelligent, as well as growing wings and a horn and gaining the ability to talk. Adora made a connection with this horse (Swift Wind), and they later became friends.
In the episode "Flowers for She-Ra", Adora accidentally transforms a small reptile, which, like Swift Wind, also gains wings and a horn. From this, Bow and Glimmer figure out what happened to Swift Wind, whom they called "Our horse," or "Horsey."