I've often wondered about the potential of the flashback to confuse people who were not familiar with the story, since it momentarily confused me, and I've known the story since it was first published in The New Yorker in 1997.
There are lots of people, maybe more on imdb than here, who thought at first it was a blooper that Jack suddenly appeared without a moustache!
As I recall Heath Ledger did not like the fact that the scene was written in a way that made him look like the sheep were more important than Jack. He didn't like the fact that he just turns away and rides off to the sheep camp,
How sweet that he thought that! Happy birthday again, Heath!
However, I think Ennis' behavior in the flashback is totally in character -- there's always that conflict between wanting to be with Jack and at the same time feeling it's his "responsibility" to ride away.
I believe this scene happened, chronologically, the night before the snowstorm that ended their time on the mountain, for reasons of symmetry and symbolism. When Ennis says "See you in the morning," then turns around and leaves, he assumes he WILL see Jack in the morning. And technically, he does -- but in a figurative way, he doesn't. In the morning there is snow, and when he next sees Jack he's tearing down the tent and their summer is effectively over and things are no longer the same between them (until the reunion).
The dozy embrace is mirrored in the lake scene, when Ennis is again driving away (apparently without looking back), and Jack is again gazing after him. Again, there is snow: snow on the mountains, snow in Jack's prediction the night before and implicitly in his complaints about the cold. Again, Ennis fully expects to see Jack "in the morning" -- that is, in November, the next time they're scheduled to get together. But this time he doesn't. After that, things will never be the same again.
To me, that elevates the phrase "see you in the morning" to a higher level of meaning. See you in the next life? See you someday in a world where homophobia won't keep us apart? I'm not saying it's meant to be literal. But it resonates so much more to think of if as the last words they exchange before not seeing each other again.