Abstract: Considering the engineering context in which lining structures in cold regions are successively exposed to freeze–thaw (F–T) cycles and cyclic dynamic disturbances during tunnel excavation, cylindrical specimens with a diameter of 50 mm were fabricated. These included pure sandstone, pure concrete, and composite specimens with sandstone layer thickness ratios of 25%, 50%, and 75%, respectively. Thereafter, constant-amplitude cyclic impact compression tests of the F–T-damaged concrete-sandstone combination were conducted using a splitting Hopkinson pressure bar system with a diameter of 50 mm. The effects of the sandstone layer thickness ratio and number of F–T cycles (0, 5, 10, 20, and 40) on the pore size distribution, stress wave characteristics (i.e., incident, reflected, and transmitted stress waves), dynamic peak stress, anti-cyclic impact times, failure mode, and micromorphology of concrete-sandstone composite specimens were investigated by integrating nuclear magnetic resonance (NMR) and scanning electron microscopy. A composite damage variable, which could consider the effects of the F–T cycle and cyclic impact, was defined based on the variation of the longitudinal wave velocity in the present study. Experimental results showed that with increasing number of F–T cycles, a notable divergence emerged in the cyclic impact resistance among the different specimen types. Specifically, the C–0% specimens maintained their original impact resistance even after 40 cycles, while the anti-cyclic impact times of both the composite and sandstone specimens exhibited varying degrees of degradation with increasing number of F–T cycles. As the sandstone layer thickness ratio increased, the number of micropores in the composite specimens decreased, while the number of mesopores increased significantly, accompanied by an increase in the dynamic peak stress. Conversely, the dynamic peak stress of specimens decreased with increasing number of F–T cycles. For the C–R–25% and C–R–75% specimens, the dynamic peak stress values without F–T treatment were 25.82 MPa and 27.87 MPa, respectively. After 40 F–T cycles, these values decreased to 19.04 MPa and 19.79 MPa, representing reductions of 26.26% and 28.99%, respectively. With the increase in the cyclic impact times, both the dynamic peak stress and dynamic secant modulus of the composite specimens decreased, while the dynamic peak strain increased. The amplitude of the reflected wave displayed an upward trend in concrete, sandstone, and concrete-sandstone composite specimens with increasing cyclic impact times, while the amplitude of the transmitted wave decreased and the occurrence of the peak value was delayed. Following cyclic impact loading, the concrete, sandstone, and composite specimens primarily exhibited two failure modes: tensile splitting and edge shear failure. The quantity and distribution of primary and secondary cracks were closely related to the sandstone layer thickness ratio within the composite specimens and number of F–T cycles. As the number of F–T cycles increased, the failure mode of the composite specimens evolved from a single main crack to multiple cracks, and the internal damage intensified within both the sandstone and concrete layers. Furthermore, distinct intergranular and transgranular cracks were observed within the sandstone layer, although no obvious damage was detected at the interface between the two layers. The “damage accumulation threshold” of concrete, sandstone, and concrete-sandstone composite specimens gradually increased with the number of F–T cycles. The findings of this study provide experimental evidence and references for analyzing the stability and durability of tunnel lining structures in cold regions.