Plant–soil biota represent a unique living system crucial for improving crops’ adaptation to climate change. In vineyards, plant–soil relations are mediated by rootstock–scion interaction, with grafted vines being the main plant material employed in vineyard planting. The interaction between two deeply different biological systems such as Vitis vinifera sativa and the American Vitis species may modify vines’ adaptation to abiotic stress. The aim of this study was to investigate the physiological response (chlorophyll content—CHL; stomatal conductance—gs) of grafted and ungrafted vines and assess the involvement of Arbuscular Mycorrhizal Fungi (AMF) in this response. In two vineyards located in Central Italy, the presence of AMF was assessed in the roots of grafted and ungrafted cv ‘Aleatico’ vines. The morphological traits of AMF and root mycorrhizal colonization differed in the grafted and ungrafted vines. Under limited climate conditions, ungrafted vines showed better leaf resilience traits (high CHL and gs values) and larger AMF storage organs (vesicles). On the other hand, the grafted ones—which are more sensitive to climate conditions (lower gs and CHL)—involved AMF colonization strategies (greater abundance of arbuscoles and mycorrhizal colonization potential) linked to the improved uptake and transport of water from the bulk soil to the vine. Taken together, these findings highlight different mycorrhizal colonization strategies and storage behaviors in grafted and ungrafted vineyards and with respect to different physical and chemical soil traits.