Curved bridges account for more than 45% of high-speed railway infrastructure, where the coupled effects of strong crosswinds and curve superelevation may significantly increase the risk of train overturning. However, the current specification Code for Design of High-Speed Railway (TB 10621—2014) only covers straight-line conditions and lacks supporting evidence in the frequency domain. A coupled dynamic model consisting of a three-car train, a 10 m-high viaduct, and a 150 mm superelevation was established. The Realizable k-ε turbulence model, together with a user-defined function (UDF) wind field, was employed to simulate aerodynamic loads at a train speed of 300 km/h, and the aerodynamic responses and spectral characteristics under steady crosswinds, random pulsating winds, and China-hat gusts were systematically investigated. The results indicate that when the wind acts from the inner side of the curve, the lateral force is reduced by 14.5%-15.4% compared with that on straight tracks, while the lift force shows a slight increase; nevertheless, the overturning coefficient is significantly increased by 33.07%-33.54%, primarily due to the variation in the aerodynamic lever arm. When the wind acts from the outer side of the curve, both the lateral force and lift force are increased by 12.6%-19.9% and 10.1%-16.6%, respectively. Frequency-domain analysis reveals that the energy of random pulsating winds is distributed over a broadband range of 0.33-8.49 Hz, dominating the low-frequency cumulative response, whereas the energy of China-hat gusts is mainly concentrated within 0.33-1.49 Hz; notably, the dominant frequency of the overturning moment is observed at 0.83 Hz, which is close to the natural frequency of the train-bridge system, thereby increasing the likelihood of transient resonance. At a wind speed of 25 m/s, China-hat gusts are found to induce the largest increase in the overturning coefficient to 33.54%, demonstrating the most significant transient impact effect among the considered wind types. This study fills the gap in frequency-domain analysis of curve-wind-superelevation coupling effects and provides a quantitative basis for dynamic speed limit design of high-speed trains operating in strong wind environments.