Trivia: The wolf in the film was played by two different wolves. Neither knew how to howl, so a third wolf had to be brought in for the howling scene.
Trivia: Kevin Costner had a nasty fall from his horse during the buffalo hunt scene, and everyone freaked out, because since he was the director, the star, and the producer, production would have shut down. Fortunately, he was fine.
Trivia: For his portrait of the Indians (which was radically different from all the earlier movies), Costner was made an honorary tribe member of the real-life Sioux.
Trivia: In the opening scene where Dunbar is supposedly lying on a operating table waiting for the surgeons to attend to his leg, this in fact is Ken Costner's film double. The man at the bottom right of the table is Costner. You never see their faces, as they walk away from the table the camera only shows their backs as not to reveal their identities, the other surgeon is Jim Wilson the producer.
Answer: He shaved it as he began spending more time with the Lakota. Native American tribes rarely accepted facial hair. As you can see, none of the other Lakota men have any. He also grew his hair longer as an abandonment of his military lifestyle.