To investigate the running safety threshold of trains on the Sichuan-Tibet Railway bridges under the floating ice impact loads, a train-track-bridge dynamics model is established based on the theory of the train-track-bridge dynamic interaction and the design method of tuned mass damper (TMD), which uses the fluid-structure coupling method to calculate the floating ice impact loads. Taking a 5 × 32 m typical simply-supported beam bridge on the Sichuan-Tibet Railway as an example, the critical train speeds corresponding to floating ice impact loads of varying intensity are evaluated, and the effect of TMD on the running safety of the trains under extreme ice loads is investigated. The results show that the fluid effect has a significant influence on the impact loads of ice hitting the bridge pier, which cannot be ignored in the calculation. The ice impact intensities significantly reduce the train's safe speeds. Under the action of floating ice impact loads, the TMD attached to the bridge can effectively reduce the train's derailment factor and wheel unloading rate. The greater the TMD mass ratio, the more pronounced the vibration control effect.