Warming winters are increasingly altering the dormancy and flowering dynamics of temperate fruit trees. In this study, we assess the adaptation potential of 22 North American sweet cherry (Prunus avium L.) cultivars to future climate conditions in Zaragoza (Ebro Valley, Spain), a representative Mediterranean-continental site. Endodormancy release and flowering were characterized over two contrasting seasons (2022–2023 and 2023–2024) to determine cultivar-specific agroclimatic requirements. Chill and heat accumulation were quantified using the Dynamic, Chilling Hours, and Utah Models for chill, and the Growing Degree Hours Model for heat. Historical trends (1974–2024) and future projections from 18 Global Climate Models (GCMs) under two Shared Socioeconomic Pathways (SSP2–4.5 and SSP5–8.5) were analyzed to assess the probability of chilling fulfillment. Historical analysis revealed a 6–8 CP decline since 1980, confirming progressive warming. The exceptionally warm 2023–2024 winter recorded the lowest chill accumulation in 50 years and was associated with flowering delays across all cultivars. Cultivar-specific analyses indicated a broad range of chilling requirements (37.6–66.6 CP), with high-chill cultivars showing increased risk of incomplete endodormancy release under warmer winters. Projections suggest that while most cultivars may remain viable by mid-century (2050), adaptation challenges will intensify by 2085, particularly under SSP5, where all cultivars show a risk of insufficient chill for at least one GCM. These findings provide empirical evidence that warming winters are reshaping sweet cherry dormancy and offer a probabilistic framework to guide cultivar selection and adaptation strategies under ongoing climate change.