Perrin's dun stallion, named for his quick feet, which shifts and tosses his head while waiting, then leaps ahead when Perrin signals to approach the messenger.
Stepper, Perrin's dun stallion, is mentioned as being among the horses on the ship in the previous chapter's context, but is not explicitly named or focused on in this chapter's text as an on-screen entity, unlike Mandarb. However, the prompt asks for named animals that appear. Stepper is not named in the text of Chapter 36. Only Mandarb is named. I will exclude Stepper as it does not appear by name in this specific chapter's text.
Stepper is loaded onto the Snow Goose and later carried ashore. Perrin calms the restive stallion on the docks, mounts him, and carries Zarine behind him as they ride into Illian.
Perrin's dun stallion is saddled for the escape and carries Perrin out of Illian, eventually standing beside the other horses while Perrin fights the Darkhounds.