I think it would be neat to have Levels in explore. Probably more of an idea for when we get new maps. Horses could have a single skill bar that along with earning regular level up points, the explore bar would only be for experience gained in Explore.

Once the horse reaches certain checkpoints on their explore bar, they could access new areas of the map, or maybe even new maps entirely. For example, only maxed level horses can explore in the mountains. Then certain items could only be found in these regions, thus making them rare, exciting to achieve, or marketable if you wish to sell.