Individual animals vary in their behaviour and reactions to novel situations. These differences may extend to differences in cognition among individuals. We tested twenty-six horses for their ability to detour around symmetric and asymmetric obstacles. All of the animals were able to get around the barrier to reach a food target, but varied in their approach. Some horses moved slowly but were more accurate in choosing the shortest way. Other horses acted quickly, consistently detoured in the same direction, and did not reliably choose the shortest way. The remaining horses shifted from a faster, directionally consistent response with the symmetric barrier, to a slower but more accurate response with the asymmetric barrier. The asymmetric barrier induced a reduction in heart rate variability, suggesting that this is a more demanding task. The different approaches used to solve the asymmetric task may reflect distinct cognitive styles in horses, which vary among individuals, and could be linked to different personality traits. Understanding equine behaviour and cognition can inform horse welfare and management.