After all Jack and Ennie were cowboys! So where is the hay fun?
Here is my long-winded explanation on this point, with some extra stuff thrown in.
First, Annie would tell you they are not cowboys, but rather ranch hands. Proulx doesn't want her story mixed up in the American popular culture myth of what represents a cowboy.
In this country, the concept of a "cowboy" is 75% cultural myth, 25% reality - more people dress like one and call themselves that than actually are, all the way up to our brush-clearing president. And most of what defines a cowboy in this country, especially the travelling with the herd, was traditionally done by folks with a questionable record, the unemployable, or almost as common - the immigrant community and African-Americans that made up to 1/3rd of the cowboy community, hired for next to nothing by ranches, especially in the post slavery period of 1865-1900.
The cowboy reality that did exist in this country was more or less dead by the early 1900s after a disastrous winter in 1906 which wiped out huge swaths of cattle herds coupled with a growing amount of formerly open property for grazing being sold off and becoming unavailable to travelling herds of cattle, which resulted in more and more herds needing to be kept closer to home. As the 20th century progressed, feed delivery and farming equipment made it possible to keep cattle on enclosed ranches, turning what used to be a cowboy into ranch employees and hands.
Proulx always emphasized Jack and Ennis served in a more authentic role of being "hands." By trying to avoid (and it frankly didn't work) the "cowboy" label, Proulx was trying to stay real, and away from doing battle with the pop culture iconography of the cowboy. The challenge of the image of the cowboy would be seen by all the usual "culture warrior" suspects as another attempt to usurp and destroy their cultural icons and images.
Proulx's efforts largely failed, and for several months in 2006 we had to endure the usual nonsense from the right wing attacking the film for its attempt to steal the notion of the cowboy (as they defined it in the terms of the cowboy myth) out from under "them." Once something gets caught up in the silly culture wars, its deeper meaning gets lost as people debate only the surface issues. I don't blame Proulx for this - the discussion was inevitable when you put two guys with western hats on horses herding anything.
Second, as far as the hay goes, sheep prefer to graze first on live broadleaf weeds, especially young and tender ones. They'll then move on to eating live grasses, clover, and young shrubs. They far prefer live plants to hay, which is fed to open grazing herds mostly in the winter when natural live foods aren't available.
A hay scene would have probably been seen as cliche (and it very much would be) and wouldn't make much sense, as there would be no reason for them to have hay up on Brokeback when there was an entire mountain pasture staring them in the face.
Ang Lee demanded authenticity on these points, which is why he went through a major nightmare of trying to get the province of Alberta to approve a domestic sheep herd grazing permit in an area shared by wild sheep in the area. Unfortunately, domestic sheep often passed on viruses and other diseases to less resistant wild sheep, and provincial officials were extremely reluctant to grant permission.
Lee managed to convince them by literally putting down fake rubber mats covered with grass where the sheep congregated so that they could be removed with the sheep and limit potential exposure. And many of the scenes in the film where sheep are seen off in the distance (and a few have them way, way off) are purely digital - the sheep were added later in the effects room.