Winans was born in Avon, New York and moved with his parents, John and Eliza (nee Way), to Michigan in 1834. The family first moved to Scio Township in Washtenaw County and in spring 1836 moved to Unadilla Township in Livingston County. His father died in the fall of 1843, and Winans moved with his mother to Hamburg Township, also in Livingston County. His mother died in July, 1852 and Winans worked for four years in a wool carding mill. At the age of twenty, he attended Albion College, Albion, Michigan, for two and a half years in preparation for entering the Law School of the University of Michigan at Ann Arbor. Before completing his studies, Winans was drawn by news of the California Gold Rush, and in March 1850 left for California by an overland route to seek his fortune. Arriving July 20, he engaged in mining first on the north branch of the Yuba River near Placerville. He continued the same work with some varied success in different parts of the state. In 1853, he was one of the members of the celebrated Randolph Hill Mining Company in the town of Rough and Ready (now a ghost town west of Grass Valley in Nevada County). He continued with the company until its dissolution in 1857. He was a principal stockholder in the Rough and Ready Ditch Company and also enagaged in banking in Rough and Ready.

He returned to Michigan in 1858 and purchased a 400 acre (1.6 km²) farm in Hamburg Township, Michigan. He was twice elected a member of the Michigan State House of Representatives 1861-1865 and was a delegate to the state constitutional convention of May 15, 1867. He was a Hamburg Township supervisor, 1872-1873 and probate judge of Livingston County 1877-1881.

Winans was elected as a Fusion candidate and seated with the Democrats in the United States House of Representatives for the Forty-eighth and Forty-ninth Congresses, serving from March 4, 1883 to March 3, 1887. He resumed agricultural pursuits in Livingston County and served as Governor of Michigan 1891-1893. He was the first Democrat elected governor after the American Civil War (Josiah Begole had been elected in 1882 on a Fusionist ticket combining the Greenback and Democratic Parties).

Winans died in Hamburg, Michigan and is interred in Hamburg Cemetery.

Winans's son, also named Edwin Baruch Winans (October 31, 1869-December 31, 1947), was a Major General in the United States Army and was commanding general of the Third Army from September 15, 1932 to September 30, 1933. He also served as superintendent of the United States Military Academy at West Point, New York in 1927.