The son of a fishing captain, Winters went to Mount Allison University in New Brunswick and then to MIT to get a degree in electrical engineering. He worked for Northern Electric, before joining the army in World War II, eventually becoming a lieutenant-colonel. He was first elected to the House of Commons in the 1945 general election as a Liberal for the riding of Queens—Lunenburg in Nova Scotia. Winters was appointed to Cabinet in 1948 and served as minister of public works among other portfolios under Prime Minister Louis St. Laurent.
Defeated along with the St. Laurent government in the 1957 election, Winters entered to corporate world becoming a Chief Executive Officer at a series of companies. He was hired as a special advisor to the Newfoundland government to help negotiate the Churchill Falls deal, for which he became highly popular in that province.
He was persuaded to return to politics by Lester Pearson, and won the Toronto seat of York West in the 1965 election, becoming minister of trade and commerce in Pearson's government. He was seen as close to the business community and far more fiscally conservative than Walter L. Gordon. He originally announced that he would not seek to replace the retiring Pearson, but changed his mind and ran to succeed Pearson at the 1968 Liberal leadership convention, coming in second to Pierre Trudeau. Winters left politics following his defeat to become president and director of Brazilian Light and Power and a vice president of CIBC. He also was much involved in the new York University serving as the first chair of its board of governors.
Winters College at York University is named in honour of him.