Update 6.4.0 adds the ability to finish building a wagon. If you have a horse, you will be able to hitch it to a wagon and choose to travel by wagon.
When you reach a location, the wagon remains next to the horse and functions as additional storage for items. If an Exile dies at a location, their horse will return home with the wagon and all its contents. Store your items there safely, since they won't vanish when you die!