My 2x great grandfather Andrew Robeson (1825-1904) was a homesteader in Nebraska in the 1880s. His first home in Furnas County was probably similar to the above picture. I don’t think I could have lived like that. They were “tougher” in them thar hills.
Monterey County Genealogy Society 
I don’t think houses like that were called “mud houses”. They were “soddies” since they were made from sod. The plains had few trees so lumber was not readily available. Soil was.