The thickness of a cover significantly influences both the bonding performance and the durability of materials against frost resistance. This research investigates the degradation and damage distribution of fundamental mechanical properties in two specimens of recycled aggregate concrete (RAC), each with varying sizes, following freeze-thaw cycles (FTCs). This comparison is facilitated through non-destructive and damage tests. Subsequently, the influence of freeze-thaw damage (FTD) on the bond strength of specimens with differing cover thicknesses is examined via pull-out tests on 14 groups of center pull-out specimens. Lastly, the bond strength is theoretically analyzed. The test results reveal that FTCs diminish the material strength of RAC, and the FTD distribution within RAC specimens is not uniform. The surface concrete sustains a higher degree of damage compared to the internal concrete, resulting in an average FTD of small-size specimens that surpasses that of large-size specimens. The residual strength of RAC can be assessed using a non-destructive test, specifically the ultrasonic wave velocity test. For center pull-out specimens, FTD not only decreases the material strength but also increases the wedge splitting angle while reducing the critical protective layer thickness. This paper proposes a soft sleeve correction theory that comprehensively accounts for the effects of FTD. When combined with non-destructive test results—namely those from the ultrasonic wave velocity test—this theory can effectively evaluate the bond strength of RAC post-FTD. This approach offers valuable insights for the design and assessment of recycled concrete in cold climates.