Wyoming has been a Republican state for nearly all of its history, mostly just leaning Republican until the 1960s. From the New Deal on, the southern counties were swingy or Democratic because of railroad and mining unions.
From 1964 on Wyoming trended Republican except the farm crisis in the 1980s and a slight backslide in 2008 to be the dark red state it is today. The darkest red counties in the northeast are very coal and oil-influenced. The Democratic areas are tourist-heavy Teton County, with Yellowstone and Teton National Parks, as well as Albany County, home to Laramie and the University of Wyoming.
Here are the results in table form.
Here are the results in map form.