How does Peyton Farquhar feel while in the water?
First, it's important to remember that Peyton Farquhar is never actually in the water. Almost the entirety of Part III occurs in his head, during the few moments between when "The sergeant stepped aside" and off the plank on which Farquhar was standing (at the very end of Part I) and when the rope snapped taut and pulled the noose tight around his neck and "his body, with a broken neck, swung gently from side to side beneath the timbers of the Owl Creek bridge" (at the very end of Part III).
However, in Part III, Farquhar imagines that while he's in the water, "He was now in full possession of his physical senses. They were, indeed, preternaturally keen and alert." He notices every quivering leaf and buzzing insect and rushing fish. He sees that the Union soldiers are firing at him, and he "dived -- dived as deeply as he could" to get away from their bullets. He swims downstream while they reload, and "His brain was as energetic as his arms and legs; he thought with the rapidity of lightning." He feels very vividly alive, with his ability to notice every tiny thing and the way his thoughts are moving so quickly.