The reactivity of interstellar carbon atoms (C) on water-dominated ices is one of the possible ways to form interstellar complex organic molecules (iCOMs). In this work, we report a quantum chemical study of the coupling reaction of C (³P) with an icy water molecule, alongside possible subsequent reactions with the most abundant closed-shell frozen species (NH₃, CO, CO₂, and H₂), atoms (H, N, and O), and molecular radicals (OH, NH₂, and CH₃). We found that C reacts spontaneously with the water molecule, resulting in the formation of ³C-OH₂, a highly reactive species due to its triplet electronic state. While reactions with the closed-shell species do not show any reactivity, reactions with N and O form CN and CO, respectively, the latter ending up in methanol upon subsequent hydrogenation. The reactions with OH, CH₃, and NH₂ form methanediol, ethanol, and methanimine, respectively, upon subsequent hydrogenation. We also propose an explanation for methane formation observed in experiments through additions of H to C in the presence of ices. The astrochemical implications of this work are: (i) atomic C on water ice is locked into ³C-OH₂, making difficult the reactivity of bare C atoms on icy surfaces, contrary to what is assumed in current astrochemical models; and (ii) the extraordinary reactivity of ³C-OH₂ provides new routes toward the formation of iCOMs in a nonenergetic way, in particular ethanol, the mother of other iCOMs once it is in the gas phase.