Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Tragic and Emotional
"Brokeback Mountain" is best defined by two things: (1) these guys really, really love each other, and (2) ain't nobody ever gonna understand. We see signs of the first one in the way they react to each other: "Jack took the stairs two and two. They seized each other by the shoulders, hugged mightily, squeezing the breath out of each other, saying, son of a bitch, son of a bitch, then, and easily as the right key turns the lock tumblers, their mouths came together […]" (47).That continues pretty much every time they see each other, even when they're angry. Proulx makes us feel how fundamental those emotions are to their being: going right down to the core without looking back.
As for the second one, we get it in the veiled comments of everyone except Jack and Ennis, from wee Lureen whose "little voice was cold as snow" (133) to Joe Aguirre who says "you guys wasn't gettin paid to leave the dogs baby-sit the sheep while you stemmed the rose" (71). That all comes on top of, you know, Jack getting beaten to death on the side of the road, so we're going to say that society isn't down with these two and their wild love.
Put them together, and you have a tone of aching, deep-set feeling tinged with a whole lot of sadness. It's grim, but so, so pretty.