Pocket Edition GUI.
Very probably related to MCPE-20351 raised on furnaces.

Just previous to the test screenshots below I noticed the inventory fence slot contents replace all four of the maps I had in hotbar slots 6-9. In inventory (I got off the horse to do this) I reorganised the four maps into inventory slot 6-9 and resynced hotbar slots 6-9 to inventory slots 6-9.

Testing from the above point onwards I re-mounted the horse and simply entered and exited the horse GUI a few times without moving anything in inventory.

Shot 1, note hotbar slot 4,5 with same instance of axe from inventory.
Shot 2, In Horse GUI, note inv slots 4,5, & 15.
Shot 3, note hotbar slot 4,5 now with same instance of leads from inv replacing axe
Shot 4, In Horse GUI, note suffling of inv slots 4,5 & 15.
Shot 5, hotbar slots 4,5 now with same instance of raw chicken replaces leads in hotbar.