Winstead was born in Sherman, Texas in 1891. Before joining the FBI he engaged in various occupations, including decorated service with the US Army in World War I, working as a deputy sheriff in several Texas jurisdictions, and just before joining the Bureau, as a law clerk in the US Attorney's office in El Paso, Texas. He joined the Bureau in July 1926.
As a member of the Dallas Field Office, Winstead took part in several unsuccessful manhunts targeting outlaws Bonnie Parker and Clyde Barrow, and played a key role in the manhunt for kidnapper George "Machine Gun" Kelly; along with Agent Gus Jones, Winstead arrested Kelly's associate Harvey Bailey in Rhome, Oklahoma, which set the FBI manhunt for Kelly in motion.
In May 1934, Winstead and several other Western agents, including former Oklahoma City policemen Jerry Campbell and Clarence Hurt, were assigned to the Chicago Field Office to help apprehend John Dillinger and his gang of bank robbers. After the Little Bohemia fiasco in April, in which agents led by Melvin Purvis and Sam Cowley had killed a civilian and lost an agent in a failed ambush of Dillinger's gang, FBI Director J. Edgar Hoover brought in the experienced Texans to augment Purvis's still-relatively inexperienced agents.
Winstead is widely believed to have been the agent who fired the fatal shot into Dillinger during the FBI's ambush at the Biograph Theater, shooting him in the back of the head at close range. For this, he received a personal letter of commendation from Hoover.
After Dillinger's death, Winstead helped track down Dillinger's former gang mate Lester Gillis/Baby Face Nelson, narrowly missing a confrontation with Nelson when he and Nelson drove past each other on a rural Illinois road. Winstead's encounter with the outlaw ultimately led to Nelson's showdown with the FBI outside Barrington, Illinois, in which both Nelson and Agents Cowley and Hollis were fatally injured.
Winstead returned west after Nelson's death, serving at the El Paso and Albuquerque offices. In 1942, he was reprimanded by Hoover for insulting a female reporter and accusing her of being a Communist sympathizer. Hoover demanded an apology and ordered his transfer to Oklahoma City; Winstead told Hoover to "go to Hell" and resigned in 1943.
After resigning from the FBI, he served as an Army intelligence and security officer in the later years of World War II. For a time, he was in charge of security at Los Alamos during the Manhattan Project, when the first atomic bomb was being constructed by the US Army.
Winstead returned to law enforcement after the war, serving various part-time jobs as a Sheriff's Deputy in New Mexico and a private investigator, before retiring and taking up horse ranching.
In the 1950s, he began work on a memoir of his years with the FBI but never finished; the manuscript was discovered in 2008 and is now kept in a museum in Sherman.
On August 3, 1973, he died in the Albuquerque Veteran's Hospital of pneumonia.
He was portrayed by actor Stephen Lang in Michael Mann's film Public Enemies (2009).