The wine industry needs better-adapted yeasts to grow at low temperature because it is interested in fermenting at low temperature to improve wine aroma. Elucidating the response to cold in Saccharomyces cerevisiae is of paramount importance for the selection or genetic improvement of wine strains. We followed a global approach by comparing transcriptomic, proteomic and genomic changes in two commercial wine strains, which showed clear differences in their growth and fermentation capacity at low temperature. These strains were selected according to the maximum growth rate in a synthetic grape must during miniaturized batch cultures at different temperatures. The fitness differences of the selected strains were corroborated by directly competing during fermentations at optimum and low temperatures. The up-regulation of the genes of the sulfur assimilation pathway and glutathione biosynthesis suggested a crucial role in better performance at low temperature. The presence of some metabolites of these pathways, such as S-Adenosilmethionine (SAM) and glutathione, counteracted the differences in growth rate at low temperature in both strains. Generally, the proteomic and genomic changes observed in both strains also supported the importance of these metabolic pathways in adaptation at low temperature. This work reveals a novel role of the sulfur assimilation pathway in adaptation at low temperature. We propose that a greater activation of this metabolic route enhances the synthesis of key metabolites, such as glutathione, whose protective effects can contribute to improve the fermentation process.