One of the best deserved oscars in Westerns went to the cinematographer of She Wore a Yellow Ribbon, Winton C. Hoch (next to William Clothier one of the best to shoot Wayne pictures, in my opinion).
Shane won a well deserved Oscar for photography as well (it was also nominated for Best Picture and Best Director among other categories)
How The West Was Won took three: for Editing, Screenplay, and Sound.
The one oscar The Alamo got was for Best Sound (not to be mistaken with the work of the composer).
For composing Dimitri Tiomkin won two for High Noon: Best Score and Best Song
Butch Cassidy won for Best Screenplay, Best Music and Best Song (Raindrops)
Stagecoach took home the Oscars for Best Music and Best Supporting Actor.
The more recent ones:
Glory won Denzel Washington the Best Supporting Actor Oscar, as well as one for photography and Sound department
Unforgiven got 4, Dances with Wolves 7.
Legends of the Fall - if you want to count it in as a kind-of-Western, won for Best Cinematography.
I think the first Western to get a Best Picture Oscar was Cimarron in 1934, as well as getting the Best Screenplay and Best Art Direction Oscars.
That's not all, but an overall view will get you the impression that Westerns most often - if at all - won for Photography.
