Due to climate change and the consequent rise in grape pH, there is often the necessity of acidifying musts or wines during winemaking. In this study, the effect of early (on musts, during fermentation) and late (on wines, after the end of the fermentation) acidification was evaluated. The experimental design consisted of the preparation of seven wines from the same batch of grapes fermented in a first tank at the original pH of 3.2 and two other tanks in which the pH was adjusted to 3.5 (3.5W) and 3.9 (3.9W). On the third day of fermentation, and one week after the end of the fermentation–maceration process, aliquots of both 3.5W and 3.9W were treated to lower pH to thus obtain four more wines. After one year of aging, wines treated so as to reach a 3.2 pH significantly differed from the control wine in terms of contents of acetaldehyde, tannins reactive towards proteins and polymeric pigments. Differences were more conspicuous when acidification was carried out after the end of the fermentation–maceration process. Data highlight that the timing of acidification has a significant effect on polymerization reactions typically occurring during wine aging.