Born in Durham County, North Carolina, on June 12, 1925, Nash Nicks Winstead attended Plainview High School near Dunn, North Carolina. From 1943 to 1946, he served in the United States Army Air Forces as a sergeant drill instructor and clerk. In 1948 and 1949, he was employed by the Smith-Douglas Fertilizer Company as a sales trainee. He married Geraldine Larkin Kelly in 1949. Winstead earned a Bachelors of Science and a Masters of Science from North Carolina State College (later North Carolina State University) in 1948 and 1951, respectively. He received his Ph.D. from the University of Wisconsin in 1953 and returned to North Carolina State College the same year, joining the faculty as an assistant professor of plant pathology. He was promoted to associate professor in 1958 and professor in 1961. He was appointed director of the Institute of Biological Sciences and assistant director of Agricultural Experiment Stations in 1965, assistant provost in 1967, and associate provost in 1973. In 1974, Winstead became provost and vice chancellor. From 1981 to 1982 he served as interim chancellor. Afterward, he continued as provost until his retirement in 1990.

Winstead was a member of Sigma Xi, Phi Kappa Phi, Omicron Delta Kappa, Torch International, the American Phytopathological Society, the American Society for Horticultural Science, and the North Carolina Academy of Sciences. He was featured in American Men of Science, Volume II, 1955 and Marquis Who's Who in America, Volume 34, 1965-66. He recieved a Sigma Xi Reseach Award in 1960 and the Ellis L. Phillips Internship Award in Academic Administration from Indiana University for 1965-66. He served on the board of trustees for the North Carolian School of Science and Math from 1985 to 1990[?], was a member of the North Carolina Council on Higher Education for Adults from 1967 to 1974, and a trustee for the Methodist Home for Children from 1980 to 1988.