Removing the armor of a horse plays the entity.horse.armor sound and shows the according subtitle "Horse armor equips", which does not fit.
The following is based on a decompiled version of Minecraft 1.10 using MCP 9.30.
The reason fro this is that the method net.minecraft.entity.passive.EntityHorse.onInventoryChanged(InventoryBasic) plays this sound if the horse had no armor and now wears armor or if the armor it wears now (including NONE) is not the same it wore before. The second condition makes little sense because this condition is already included in the first one. I assume something like following is the intended behaviour:
Note: Changing the armor to a different armor item of the same type does not play the sound which could be seen as a bug.