The Curse of Binding enchantment does not function on horse armor.

In contrast to the Thorns, Feather Falling, Curse of Vanishing, Depth Strider (before 1.20.5 MC-268934), and Respiration (before 1.20.5 MC-268934) enchantments, the Frost Walker enchantment does not work when applied to horse armor. You can remove it from the horse in survival mode!