During Hayden's expedition of 1877, Yount engaged in mountaineering with Ingersoll and the cartographer A. D. Wilson in the Wind River Range. They were the first to ascend the south slopes of Wind River Peak, and, with Wilson, Yount was the first to ascend West Atlantic Peak. Hayden's expedition of 1878 conducted surveys in Yellowstone National Park and surrounding areas in 1878. That expedition included the British mountaineer James Eccles and Eccles's favorite Swiss mountain guide, Michel Payot of Chamonix. Eccles wanted to attempt an ascent of the Grand Teton, then unclimbed. This was the third attempt to climb the Grand Teton by members of Hayden's expeditions. Yount served as the guide in a four-man party that included Eccles, Payot and Wilson. Eccles and Payot were held up by the disappearance of two mules carrying their gear, and so were unable to accompany Wilson and Yount on to the higher parts of the mountain. During the climb, Yount slipped on the ice and fell close to a deep chasm in the glacier, where water was streaming down from the cliff above. The hold of his buckskin pants on the ice reportedly prevented him from being carried down into the crevice. Wilson was quoted as saying that Yount was clinging to the rock like "a starfish hanging to a breakwater," and that he himself lowered a rope to assist Yount. Because of the delay and the absence of the experienced Alpine climbers, Yount and Wilson had to turn back a few hundred feet short of the summit, at a spur called The Enclosure. No previous party had come so close to reaching the summit. The undisputed first ascent of the Grand Teton took place 20 years later, in 1898.