The winged horse in The Magician’s Nephew is Fledge.
Fledge begins the story as Strawberry, the cab-horse belonging to Frank, a London cabby. After Strawberry is transported to the newly created Narnia with Digory, Polly, Frank, and others, Aslan gives selected animals the power of speech. He then asks Strawberry whether he would like to become a winged horse.
When Strawberry agrees, Aslan transforms him and gives him the new name Fledge. Fledge carries Digory and Polly across Narnia to a distant mountain garden, where Digory must retrieve a magical apple. The journey is essential to the plot: the apple will help protect the young Narnia and later helps heal Digory’s sick mother.
Readers sometimes confuse Fledge with Pegasus, the winged horse of Greek mythology, because both are flying horses. Pegasus is not the horse’s name in Lewis’s novel. Hwin and Bree belong to later Narnian adventures, particularly The Horse and His Boy, while Fledge is associated with Narnia’s creation and is described as the father of its flying horses.