Graham Greene did not receive an Oscar nomination for portraying Walter Crow Horse in Thunderheart.
Well before I get to another 25 year break, here is a different one. Before Graham Greene played a harried overworked police officer on a reservation in Wind River, he played one in this film. Although both films begin with the same basic premise, they differ very much in content and theme with this film following far more closely the greater implication of the murder here as the film is as much about the conflict between the FBI, the various factions of the reservation, with the murder just a starting point. Technically speaking Graham Greene's performance most directly relates to the murder though as we first meet him as he comes to pick up the body running afoul of FBI veteran Frank Coutelle (Sam Shepard) and novice investigator Ray Levoi (Val Kilmer) put on the mission due to his minor Sioux heritage. Any initial misunderstandings are cleared up though as Walter is revealed to the law on the reservation. Greene makes the right impact right off the bat though in his comical exasperation towards Ray Levoi's over eagerness, and he establishes his approach to Walter.
Greene on one hand is quite entertaining in giving a quietly comedic performance, what he'd do again in his similair role in Wind River. Greene is able to find the right balance here though in his low key way of infusing some truly natural humor in the role. He never tries to be funny but rather just is. This is often just in his reactions towards Ray early on as he shows that Walter in no way expects Ray to be all that much help. Greene effectively delivers the way Walter goes about pestering Ray a bit early on in a way as he grants the character the right confidence in his peculiar sort of authority over the man. The moment where he pulls over Ray for speeding, though with the intention to speak to the man, Green though has the right sort of fun in the moment showing the bit of honest enjoyment that Walter gets out of mocking Ray a bit. Although Greene manages to be funny in the role that is in no way his point in the film, as he has the far more important part of being essentially Ray's guide into the world of the reservation helping him see an alternate view beyond what Coutelle tells him.
Greene makes Walter the moral guide of sorts to Ray, even though he is also the most entertaining character though even that Greene shows that his certain comic exasperation comes from a place of real pain over his thankless job in a terrible situation. After awhile Greene shows the little jokes, while always have a bit of genuine anger, eventually have a bit of wisdom in them as well. Greene finds the right balance in his performance showing Walter own devotion to his quest though he goes about it in his own way. Greene's terrific in the way he actually eases up a bit in his sort of trolling of Ray as the situation becomes more dire and Ray begins to learn the truth. Greene in his approach slowly brings a greater gravity and direct passion. Again not something that was not there before but Greene powerfully brings it to the forefront when it becomes the most important. He quite honestly delivers the transformation for Kilmer's character more than Kilmer himself, as he makes an impact through the way Walter reacts to the man making so much out of the respect for the man he reveals in his eyes. This is a strong performance by Graham Greene, and even though I think the film could have made an even better use of his character particularly in relation to Kilmer's, his work still stands as the highlight of the film.