Many northern hemisphere countries have experienced exceptionally heavy snow, blizzards, and cold snaps in recent years, causing considerable public concern about the high crash rate and safety issues in road traffic. This study used the CarSim dynamics simulation to recreate several vehicle driving scenarios in snow and ice conditions. To explore the influence of speed, curve radius, and road adhesion coefficient on vehicle sideslip and rollover, four lateral stability evaluation indicators, namely lateral offset, lateral acceleration, yaw rate, and roll angle, are chosen. Unfavorable combinations of these factors result in vehicle deviation from their intended trajectory and dramatically increase the likelihood of sideslip and rollover incidents. In particular, road adhesion coefficients ranging from 0.10 to 0.20 lead first to sideslip, while coefficients of 0.21 to 0.35 lead straight to rollover. Additionally, in the initial segment of the curve, cars are more susceptible to lateral instability. Curve radius has the greatest influence on sideslip when the three influencing factors are combined, while speed is the key component affecting rollover incidents. Smaller curve radii and higher speeds are major factors in such incidents. The results are helpful for proper road alignment parameter selection and dynamic speed-limit measures. This can provide a theoretical basis for traffic management departments to take targeted measures, which is of great significance to improving road traffic safety in snowy and icy weather.