Ensuring the safety of large curved-roof structures subjected to blizzards in cold regions remains challenging. This paper assesses the reliability of a large curved-roof structure considering the coupled effects of wind and snow. To this end, a two-way coupled simulation considering the interaction between snow particles and turbulent wind is first carried out using a computational fluid dynamics scheme and a spectral representation method based on the wavenumber-frequency joint power spectrum and stochastic harmonic function; thereby, the uneven snow distribution and stochastic wind field on a large curved roof are revealed. The probability density evolution method is then adopted to conduct a stochastic response and reliability analysis of the structure. The simulation results reveal that a credible uneven distribution of snow on the large curved roof can be obtained using the suggested snowdrift simulation scheme, and the refined spectral representation method can efficiently and accurately simulate the two-dimensional fluctuating wind field of the large curved-roof structure. It is shown that under stochastic wind, snow and self-weight loads for a 100-year return period, the large curved-roof structure has a higher risk of member yielding than of node deflection. Meanwhile, the axial stress acting on the structural member is far less than the maximum allowable stress and the structure is thus deemed to be sufficiently safe.