In this study, we performed small-angle X-ray scattering (SAXS) to investigate the structure of Nafion® membranes. The effect of freeze/thaw (F/T) cycles (from ambient temperature down to −40 °C) on the membrane nanostructure was considered for the first time. The SAXS measurements were taken for different samples: a commercial Nafion® 212 membrane swollen in water and methanol solution, and a water-swollen silica-modified membrane. The membrane structure parameters were obtained from the measured SAXS profiles using a model-dependent approach. It is shown that the average radius of water channels (Rwc) decreases during F/T cycles due to changes in the membrane structure as a result of ice formation in the pore volume after freezing. The use of water-methanol solution (methanol content of 20 vol.%) for the membrane soaking prevents changes in the membrane structure during F/T cycles compared to the water-swollen membrane. Modification of the membrane surface with silica (SiO2 content of 20 wt.%) led to a redistribution of water in the membrane volume and resulted in a decrease in Rwc. However, Rwc for the modified membrane did not decrease with the increasing number of F/T cycles due to the involvement of SiO2 in the sorption of membrane water and, therefore, the prevention of ice formation.