Wyoming is known as the "Equality State," even though it proved itself to be an unfriendly place for homosexuals in 1998, when Matthew Shepard was beaten to death and left tied to a fence post. (Source)
And the threat of that violence echoes in Brokeback Mountain: Ennis remembers two old cowboys who lived together…until one of them is beaten to death, castrated, and dumped in a ditch.
In fact, as far as Brokeback Mountain is concerned, the one thing Wyoming has in its favor is that it's downright gorgeous, and Rodrigo Pietro, the film's cinematographer, lingers on the state's lush landscapes. But the majestic panoramas aren't just eye candy. The scenery often mimics the mental landscape of the film's main characters.
Cowboys long for freedom, and nothing is freer than the sweeping Wyoming vistas. There are unpredictable weather patterns, like Jack and Ennis's tumultuous relationship. The mountains are like the speedbumps in their relationship, breaking up the flat plains. And the mountains are often reflected in the rivers, as the characters are searching for their own identity, and often finding themselves reflected in each other.
The time period is also important. Wyoming's still rural today, but it was even more off the grid back when the movie was set. Time passing is done subtly, either through dates stamped on postcards or the aging makeup applied to the actors. The twenty-year span, along with the breathtaking landscapes, create an epic feel for what's an epic love story.