A systematic mechanistic survey was performed for the CH₃OH + OH reaction on ice. ONIOM(ωB97X-D/Def2-TZVP:AMOEBA09) calculations suggested a range of binding energies for the CH₂OH radical (0.29–0.69 eV) and CH₃OH (0.15–0.72 eV) molecule on hexagonal water ice (I_h) and amorphous solid water (ASW). Computed average binding energies of CH₂OH radical (0.49 eV) and CH₃OH (0.41 eV) are relatively stronger compared to the CH₃O radical binding energies (0.32 eV, Sameera et al., J. Phy. Chem. A, 2021, 125, 387–393). Thus, the CH₃OH molecule, CH₂OH and CH₃O radicals can adsorb on ice, where the binding energies follow the order CH₂OH > CH₃OH > CH₃O. The multi-component artificial force-induced reaction (MC-AFIR) method systematically determined the reaction mechanisms for the CH₃OH + OH reaction on ice, where two reaction paths, giving rise to CH₂OH and CH₃O radicals, were confirmed. A range of reaction barriers, employing the ωB97X-D/Def2-TZVP level of theory, was found for each reaction (0.03–0.11 eV for CH₂OH radical formation, and 0.03–0.44 eV for CH₃O radical formation). Based on the lowest energy reaction paths, we suspect that both reactions operate on ice. The computed data in this study evidence that the nature of the binding site or the reaction site has a significant effect on the computed binding energies or reaction barriers. Thus, the outcomes of the present study will be very useful for the computational astrochemistry community to determine reliable binding energies and reaction barriers on ice.