Research on the damage and fracture mechanism of freeze-thaw (F-T) rocks under loading is a key scientific endeavor derived from numerous safety concerns in cold region rock mass engineering. This study analyzed the relationship between the entire triaxial compression process of the red sandstone and acoustic emission parameters. Based on the nonlinear growth characteristics of cumulative event counts of acoustic emission, a predictive method was proposed for determining the crack initiation strength, damage strength, and failure strength of F-T sandstone. The results demonstrated that this method exhibited good consistency with the crack volume strain approach and accurately and conveniently predicted sample failure strength. The fitted curve of the equation closely aligned with experimental data. These findings offer insights into the classification of damage and fracture mechanisms in F-T sandstone and provide valuable groundwork for research on rock failure prediction and forecasting methods employing acoustic emission monitoring.