"I'll have to do some thinking on the dozy embrace with the hats on. All I can think of is the colors in their hats are like the yin and the yang and they are touching. There's an exception to every rule Miss-Red."
Yes, that is a challenge, isn't it...
As everyone else has said, keep in mind that you don't follow all the symbolic gestures all the time. And the hats in the dozy embrace certainly made it stand out as different.
Let's think about the SNIT for a minute as a contrast. Ennis very obviously, very memorably, takes his hat off his head... but then he holds it in front of his, um, pelvis like a shield, then over his chest (heart), until Jack takes it away, gently but firmly (Jack hatless and shirtless here of course), and they open up to each other much more intimately than during the FNIT.
Now back to the dozy embrace. A famous part of the story describes that embrace as as satisfying a "shared and sexless hunger"; at that moment Ennis would not have felt comfortable embracing Jack from the front. So the hats being on can show that the embrace was not a full-on, hat-knocking-off imbroglio like the reunion embrace.
Ever so slightly off topic: in the dozy embrace, I have often thought it odd that Ennis strokes the jacket lapel, not the face or even the shirt. Once again, perhaps in an attempt to the be (somewhat) faithful to the story's description of a "sexless" embrace, the hats and the jackets provide a little insulation against sexuality for the characters (and the viewer). (However, it must be said that the dozy embrace does look to me very much like the embrace of lovers... but still, perhaps, "sexless" at that moment.)