Henry Fonda did not receive an Oscar nomination for portraying Gil Carter in The Ox-Bow Incident.
Henry Fonda plays one of the men in the posse although he is rather different from most of the men. His character Gil Carter, although originally from the rough dead end town, is now an outsider who only goes along with the posse so that he and his friend (Harry Morgan) are not accused of anything themselves. There isn't anything particularly special about Fonda's performance early on as he just is a fairly standard type of main character who occasionally gets a little agitated by the stupidity of some of the towns' folk around him. It is fairly limited, but to Fonda's credit he does play it exactly as he should.
As the film proceeds the film almost becomes an ensemble piece. Fonda is the lead of the film, but really just barely leading. Fonda though his consistently solid in his portray of Gil, and does well in portraying his character's fairly cynical outlook during the whole process of deliberation on whether or not to lynch the man. Fonda's expression of defeat conveys a lot of almost an acceptance of the terrible deeds of the others, but importantly there are the pivotal moments where Gil does speak up passionately against the wrongs committed by the posse. These are short moments for sure but Fonda gives them the strength they need through his almost trademark righteous passion.
His best scene in the film doesn't come in one of his louder passionate moments but instead a quiet scene as he reads the letter of one of the condemned men to the lynching party. Fonda delivery of this scene is fantastic as he brings the poignancy to the scene in an effortless fashion. It is a great moment as through his performance he brings out the beauty of the words that are filled not with moral outrage but rather a sadness and pity for the terrible deeds committed by the men. That scene makes this a memorable turn by Henry Fonda. Otherwise he mostly serves his character and the film just as he should even though he is mostly overshadowed. The true power of this film belongs to another performance which I will be getting to very soon.