A key question in the field of animal cognition is how animals comprehend their physical world. Object permanence is one of the fundamental features of physical cognition. It is the ability to reason about hidden objects and to mentally reconstruct their invisible displacements. This cognitive skill has been studied in a wide range of species but never directly in the horse (Equus caballus). In this study, we therefore assessed the understanding of visible and invisible displacements in adult Welsh mares in two complementary experiments, using different horses. In experiment 1, visible displacement was investigated using two tasks adapted from the Uzgiris and Hunt scale 1. Invisible displacement was assessed using a transposition task, in which food was first hidden in one of two containers and the location of the containers was then switched. In experiment 2, we further investigated horses' understanding of visible and invisible displacements using an easier procedure designed to avoid potentially confounding factors. In both experiments, horses successfully completed the tasks involving visible displacement with two or three possible hiding places. However, in both experiments, horses failed the transposition tasks, suggesting that they may not be able to track the displacement of an object that is not directly perceived (i.e., invisible displacement). These results bring new insights into object permanence in horses and how they represent their physical world.