I think it's fair to assume Ennis DOES show emotion at the news of Jack's death, but Ang just didn't happen to film it. Mainly, I think, to enhance the drama of the closet scene. But also to show that Ennis is expert at controlling his emotions around other people -- which is not the same as saying he doesn't feel them. Think of how calm he is when he parts with Jack after Brokeback, but then he goes into the alley ...
The post office scene cuts off just after Ennis spends enough time reading the "deceased" to absorb its meaning. Then it picks up again some time later, in the phone booth. Who knows what happened in between? During the phone call, he is actually fairly emotional, by Ennis' standards. For instance, right hearing how Jack died, he can't speak and Lureen says, "Hello? Hello?" And after she hangs up, he doesn't just replace his own receiver and calmly go about his business -- he looks disparingly out the window (metaphor for thinking of Jack) and clutches the receiver. Again, the scene cuts off immediately, so who knows what he did after that.
Even at the Twists' ranch, while sitting at the kitchen table, he shows a lot of emotion. But as usual it's pretty tightly controlled, expressed in just the tiniest changes in his facial expression.
It's impossible to know exactly how he behaved during the times that the camera wasn't on him. But in any case, I think we can say that if we'd seen him sobbing uncontrollably in the post office scene and again in the phone booth and again in the truck as he's driving to the Twists, the emotional power of the shirt scene would be considerably undercut.