On curved slopes covered with water, snow or ice, vehicles are prone to skidding and losing control during braking, which is a critical traffic safety issue that needs to be addressed in rainy or cold regions. The characteristics of tire-road friction capacity demand of vehicles on low-friction curved slopes were first analyzed. Based on this, the geometric design parameters of highway horizontal alignment, vertical alignment, and cross slope—were integrated with driving mechanical factors such as road friction coefficient, tire rolling resistance, and aerodynamic drag to derive the relationship between vehicle speed and maximum achievable braking deceleration. Considering the braking slip ratio, a predictive model for the minimum braking distance on low-friction curved slopes was proposed, and the model was validated through CarSim-based vehicle dynamics simulations. The study can provide a reference for the coordinated optimization of speed and braking deceleration of autonomous vehicles on low-friction curved slopes, and also offer support for car-following safety assessment and risk warning on interchange ramps in rainy or snowy regions.