You mean like Ned or Robb Stark, or John Snow; all of whom have multiple skills, are well-learned, persuasive, and can survive in the wilderness, track, sneak, ride, and are reasonably athletic?
Or the many knights of Arthurian and other Chivalric romance who are almost always skilled woodsmen AND accomplished courtiers in addition to being skilled combatants and accomplished riders?
Or the Samurai of Japanese legend (and reality) who were expected to cultivate artistic pursuits in addition to being able to use weapons well, both on horseback and not?
Or the various characters in "The Thirteenth Warrior," say? Many of whom were skilled in things other than just fighting. ALL of them were reasonably stealthy, perceptive, trained sailors, and soldiers who could ride horses and build siege defenses. Yes, they all had specialties, but like Roman Legionaires, they're definitely more than just combatants.
And then there's all the heroes of Greek myth and legend, most of whom are basically just fighters (albeit also often demigods), including Achilles, Odysseus, Hercules, Perseus, Theseus, Jason, and the rest of the crew of the Argo.
And I think that case can be made for just about ALL of the "Fighter types" in legends and fiction. Yes, they are skilled combatants, but that alone doesn't define them.