This simple vernacular form probably dates to the 19th century. The well house is later, but a notable survivor.
Thanks to Sylvette Walsh for suggesting this photograph. I don’t know how old the well is, but it’s right in the middle of the street in downtown Omaha. She notes that about 20 years ago, the well was a wooden construction with the traditional roof covering. Janice Morrison-Williams wrote that the structure behind the well, which I thought was a store, was actually the old post office.