We studied the temperature dependence of the transfer rate of a proton from excited-state 8-hydroxy-1,3,6-pyrenetrisulfonate (HPTS) to the solvent in methanol-doped ice over the wide temperature range of 80-268 K. Ice is a poor solvent, and therefore methanol is used as an amphiphilic cosolvent to dissolve the large HPTS molecule in ice. Time-resolved and time-integrated emission spectra are used to evaluate the rate of the proton transfer process, which decreases with a decrease in the temperature. We found that at temperatures below 173 K and at high methanol concentrations above 1% mole ratio the proton transfer rate is at least 10 times slower than the radiative rate, and consequently could not be detected clearly. The temperature dependence of the proton transfer rate constant, kPT, at T > 173 K cannot be described by a single mechanism of an activated process. We therefore used tunneling calculations to fit the values of ln(kPT) as a function of the temperature. Below 173 K and at low methanol concentrations, < 1% mole ratio, we found that the proton transfer process indeed occurred. The process is independent of the temperature, and strongly depends on the methanol concentration. The kinetic isotope effect of H+/D+ is large at T < 173 K and strongly depends on the methanol concentration.