Swasey's Cabin
Sounds like it was a "Line Shack"

"The Swasey brothers, Joe, Sid, Charley, and Rod, were some of the early cattlemen that explored the San Rafael Swell while running cattle there in the late 1800s and early 1900s. You find their names on many features in the Swell such as Sid and Charley Tower, Joe and His Dog, Sid's Leap, etc. The stories and places they have roamed have given them a larger than life persona. It is hard to imagine wandering the Swell when it was so remote and little known.

In 1921, Joe Swasey built what is known as Swasey's Cabin in the heart of the Swell. The cabin was to be used as shelter by the Swasey's and other cowboys when running cattle in the area. Almost 100 years later, the cabin still stands in its picturesque spot near Broken Cross Tower."

Got to put that on the Places to Visit list!