While crumb rubber powder has demonstrated effectiveness in enhancing the mechanical properties of asphalt binders, its viscoelastic behavior under freeze–thaw conditions in clean water and de-icing salt, typically urban road conditions in winter, remains insufficiently explored. This study systematically investigated the microstructural evolution, compositional changes, and mechanical behavior of asphalt modified with rubber under the influence of freeze–thaw conditions in clean water and de-icing salt. The findings revealed that rubber powder incorporation accelerates the precipitation of oil, enhancing material stability in both aqueous and saline environments. Notably, asphalt containing 10% crumb rubber powder (Asphalt-10% RP) and 20% crumb rubber powder (Asphalt-20% RP) exhibit creep recovery rates 50.53% and 28.94% higher, respectively, under de-icing salt freeze–thaw cycles than under clean water freeze–thaw cycles. Therefore, in regions with extremely low temperatures and frequent snowfall, rubber powder exhibits significant research potential, providing theoretical support for the design of asphalt pavements in cold climates.