I don't think it's angry so much as disappointed. He was probably looking for Nix to tell him about the demotion, but he shows up seeming very casual about the whole thing and talks to Nix instead of just telling him right off that he's been demoted and is even jealous of Nix going off to do the combat jump while he was stuck at a meeting. I almost feel like Winters would be jealous of the demotion because he'd like to be with the men still, but there's nothing he'd ever do to warrant it.