This list looks great. I predict I'll end up giving Red River 3 stars. It looks like one of the better John Waynes. I think it won Best Picture didn't it?
No,
Red River did not win Best Picture. It wasn't even nominated. That year Olivier's
Hamlet won Oscar's Best Picture (John Huston won Best Director for
Treasure of the Sierra Madre). The only two Academy Awards
Red River was up for were Best Writing and Best Editing. It won neither.
The only Westerns to win Best Picture to date are
Cimarron (1931),
Dances with Wolves (1990), and
Unforgiven (1992). Plus
No Country for Old Men (2007) if that fits your definition of a modern Western.
Red River was not nominated. Nor was
The Searchers. Of that classic era of the '40s and '50s the only Westerns nominated for Best Picture were
Stagecoach, The Ox-Bow Incident, The Treasure of the Sierra Madre, High Noon, Shane, Seven Brides for Seven Brothers, Friendly Persuasion, and
Giant.
The Alamo, How the West Was Won, and
Butch Cassidy and the Sundance Kid were the only nominees in the '60s, there were none in the '70s or '80s, and since the two wins in the early '90s there has only been
Brokeback Mountain, True Grit, Django Unchained, The Revenant, and
Hell or High Water.
There are a few big acting wins from Westerns: Gary Cooper as Best Actor for
High Noon, Wayne got his Best Actor for
True Grit, DiCaprio got his for
The Revenant, and Daniel Day-Lewis' Daniel Plainview towers above them all in
There Will Be Blood. Lee Marvin won Best Actor for his dual role in the comic Western
Cat Ballou and going back to the first couple years of the Oscars Warner Baxter was named Best Actor for playing The Cisco Kid in
In Old Arizona. There were a bunch of winners for Best Supporting Actor from Westerns, too: Thomas Mitchell in
Stagecoach, Walter Brennan in
The Westerner, Walter Huston in
The Treasure of the Sierra Madre, Anthony Quinn in
Viva Zapata!, Burl Ives in
The Big Country, Melvyn Douglas in
Hud, Jack Palance for
City Slickers, and Christoph Waltz for
Django Unchained (plus Javier Bardem in
No Country for Old Men).
Patricia Neal's Best Actress for
Hud is the only female role in a Western to earn an Oscar. There have only been a handful of nominees including Julie Christie for
McCabe & Mrs. Miller, Mary McDonnell for
Dances with Wolves, Irene Dunne for
Cimarron, Mercedes McCambridge for
Giant, Lillian Gish and Jennifer Jones for
Duel in the Sun, Hailee Steinfeld for
True Grit, and Madeline Kahn for
Blazing Saddles.