Considering the randomness of fluctuating wind, reliability theory was applied to calculate the failure probability of a train passing through a curve under different mean wind speeds. The operational safety of the train under crosswinds from both the inner and outer sides was analyzed, and the wind speed-train speed operational safety domain under different failure probabilities was established. Firstly, the unsteady aerodynamic load on the train was simulated by using the harmonic superposition method with the wind speed power spectral density function. The Chinese high-speed railway ballastless track spectrum was selected as the track irregularity excitation. Secondly, a multi-body system dynamics model of the train was established using SIMPACK. The aerodynamic load and track irregularity were applied as external excitations. The safety evaluation indicators of the train passing through the curve at different speeds under different mean wind speeds were calculated. The wheel load reduction rate was found to be the most sensitive to changes in speed and wind speed. Finally, based on reliability theory, the wheel load reduction rate was used to construct a performance function. A surrogate model based on support vector machine regression was employed to fit the limit state equation. The failure probability of train operation under different wind speeds and train speeds was calculated. The inner and outer wind safety domains of the train under different probabilities were obtained and compared with the train curve-passing safety domain derived from traditional deterministic methods. The results indicate that when the train speed remains constant, a larger failure probability corresponds to a larger wind speed safety domain. Under external crosswinds, the safe wind speed first increases and then decreases as the train speed increases, while under internal crosswinds, the safe wind speed consistently decreases with increasing train speed. At lower train speeds, external crosswinds result in lower safe wind speeds compared to internal crosswinds, whereas at higher train speeds, internal crosswinds lead to lower safe wind speeds than external crosswinds. Compared to the safety domain obtained using traditional deterministic methods for train curves, the probabilistic characteristic wind curve calculated using reliability methods for trains better reflects the variation of safe wind speeds with train speed.