The frost resistance characteristics and deterioration law of rock masses under freeze–thaw cycles in cold regions are important prerequisites for engineering design and stability analysis. In traditional experimental research, there exists the problem of sample selection bias caused by the heterogeneity and anisotropy of the original rock samples, which leads to a large dispersion of experimental results. To mitigate this problem, using red sandstone in Ezhou as the target object, this research first established a similarity criterion formula. Then, to obtain reliable experimental results, 3-factor and 5-level orthogonal experiments were designed with the water-cement ratio, weight ratio of quartz sand and cement, and silica fume content as control factors. Finally, a freeze–thaw cycle experiment was conducted. Based on the control indices of strength and porosity, preliminary screening of the proportion was subsequently carried out by comparing the parameters of the original sandstone, and 3 schemes stood out consequently, based on which the freeze–thaw cycle experiments were conducted. Eventually, according to the similarity criteria and sensitivity factors such as weight, wave velocity and strength, the optimal quasi-sandstone material proportion scheme was determined as follows: water and cement ratio (0.42), quartz sand and cement ratio (1.1), and silica fume content (0.1%). The experimental results further reveal the deterioration law of sandstone under freeze–thaw cycles, which indicates that with the increase in freeze–thaw cycles, the frost resistance parameters of sandstone show a downward trend, and the frost resistance gradually decreases. The descending order of the sensitivity of the frost resistance indices of sandstone to the effect of freeze–thaw cycles is the strength deterioration coefficient, wave velocity deterioration coefficient, and weight loss ratio.