Greenhaw was born in Dallas, Texas[7] in 1954. He learned to play the guitar at age eight, and by fourth grade had his own band, "The Doodlebugs". He played in a rock band named "The Inner Soul",[8] where he met physician George Miller, father of rock musician Steve Miller. The elder Miller hired Greenhaw's band to play at parties,[8] and Greenhaw's interest in guitar led him to country music. He also studied classical music as a child, and he was part of the first group of students admitted by audition to Southern Methodist University's (SMU) newly created Piano Preparatory Department. He was eventually taught by Lucien Leinfelder.[9][10] Greenhaw received his bachelor's degree in political science from SMU in 1976.[11]
From 1983, Greenhaw was musical director and band leader of a weekly country music revue, the Mesquite Opry. He first worked with the Light Crust Doughboys when he booked them to play at the Mesquite Folk Festival in 1983, which he had founded.[11] Walter Hailey, the Doughboys' master of ceremonies in the 1950s, was born in Mesquite and was a friend of Greenhaw's family.[12]
The band had been working only sporadically for several years. Greenhaw became their bassist, co-producer, and manager in 1993. He arranged for the band to play in theaters throughout Texas and Oklahoma, and brought his experience as a rock bassist to their musical style. He organized performance and recording opportunities for the Doughboys. In 1997, he took the lead in composing and arranging music and recording the soundtrack for the documentary film Lugosi: Hollywood's Dracula [13], about actor Bela Lugosi. He worked on the project with University of Oklahoma instructor Gary Rhodes.[14] The project received a positive review in Filmfax magazine.[15]
Also in 1997, the Doughboys joined the Southern Methodist University Mustang Band[16] and worked on a recording entitled The High Road on the Hilltop. This collaboration came through Greenhaw's previous connections with SMU. His father, Frank, earned a degree from SMU and from 1941 to 1945 was student director of the SMU Mustang Band.[8] Greenhaw wrote three of the songs that were recorded, "High Road", "Texas Women" and "Hangin' 'Round Deep Ellum".[17]
The 2005 album 20th Century Gospel: From Hymns to Blackwood Brothers Tribute to Christian Country, included contributions from Greenhaw and the Light Crust Doughboys, as well as The Jordanaires and Nokie Edwards. AllMusic said the album was "A pristinely recorded and expertly played slice of truly American music . . . an uplifting work that resonates with the participants' obvious love of making music."[18]
In 2006, for the Diamond Anniversary of the Light Crust Doughboys, America Sejung Corporation (ASC) were commissioned to produce a limited edition series of seven fretted musical instruments. With Greenhaw as technical advisor, they included a banjo, mandolin (with pickup), electric bass, and hollow and solid-body electric guitars. The instruments were produced in a customised "Biscuit Brown" colour.[19][20][21]
Greenhaw was inducted into the Texas Gospel Music Hall of Fame in 2015 at Dallas Baptist University, in Dallas, Texas.[22] In 2015, his book, Mesquite (Images of America), was released by Arcadia Publishing.[23]
In 2016, Greenhaw began creating, editing and writing faith-based visual novels and comic books, starting with a book series titled God's Silver Soldiers[24] (also known as Silver Soldiers: The Comic), and followed by Tales of Nazareth: The Boyhood of Jesus.[25] The comic books, under the imprint of Truthmonger Comics Group Publishing, were praised for their innovative illustrations as well as their storylines and received media coverage.[26]