I have always thought Ennis kills two coyotes: the one with balls the size of apples, and the one that killed the sheep while Ennis was having TS1 with Jack.
Why Ennis was hammerin' the first night, but then jacketless the second: By the time he crawls into the tent for TS1, it's very, very late at night, he's been sleeping directly on the ground, with no fire. The very next night, for TS2, I picture that they are going to bed basically directly after dinner. He's been sitting up off the ground by a warm fire, and the sun has only been set for a while. And they are highly motivated to be wearing as little as possible.