Severe winds produced by thunderstorm downbursts pose a serious risk to the structural integrity of wind turbines. However, guidelines for wind turbine design (such as the International Electrotechnical Commission Standard, IEC 61400-1) do not describe the key physical characteristics of such events realistically. In this study, a large-eddy simulation model is employed to generate several idealized downburst events during contrasting atmospheric stability conditions that range from convective through neutral to stable. Wind and turbulence fields generated from this dataset are then used as inflow for a 5-MW land-based wind turbine model; associated turbine loads are estimated and compared for the different inflow conditions. We first discuss time-varying characteristics of the turbine-scale flow fields during the downbursts; next, we investigate the relationship between the velocity time series and turbine loads as well as the influence and effectiveness of turbine control systems (for blade pitch and nacelle yaw). Finally, a statistical analysis is conducted to assess the distinct influences of the contrasting stability regimes on extreme and fatigue loads on the wind turbine.