Freeze–thaw cycling has a significant impact on the energy utilization and stability of roadbed fill. Given the good performance of basalt fiber (BF) and plant fiber (PF), a series of indoor tests are conducted on fiber-reinforced red clay (RC) specimens to analyze the shear strength, thermophysical, and microstructural changes and damage mechanisms of the RC under the freeze–thaw cycle–BF coupling, meanwhile, comparing the improvement effect of PF. The results indicate that the RC cohesion (c) first increases and then decreases with the increasing fiber content under BF improvement, reaching the maximum value at the content of 2%, and the change in the internal friction angle (φ) is relatively small. As the number of freeze–thaw cycles increases, cohesion (c) first decreases and then gradually stabilizes. The thermal conductivity increases with increasing moisture content, and the thermal effusivity increases and then decreases with increasing moisture content and fiber content. The heat storage capacity reaches the optimum level at a moisture content of 22.5% and a fiber content of 1%. Microanalysis reveals that at 2% fiber content, a fiber network structure is initially formed, and the gripping effect is optimal. The shear strength of PF-improved soil is higher than that of BF at a fiber content of 4–6%, and the thermal conductivity is better than that of BF. At the same fiber content, the heat storage and insulation capacity of BF-improved soil is significantly higher than that of PF.