Stepper
Chapter 1 - Waiting
Stepper
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.
Chapter 35 - The Falcon
Stepper
Perrin's dun stallion, Stepper, is among the horses led behind Lan to the river and subsequently lifted aboard the Snow Goose.
Chapter 36 - Daughter of the Night
Stepper
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.