To ensure driving safety in adverse weather conditions, this paper examines traffic flow during foggy days as a case study. Using cellular automata, it explores the critical features of three-phase traffic flow under such conditions. Initially, the impact of moderate fog on driving behavior and vehicle motion is analyzed. Next, the effect of brake lights on drivers is incorporated to enhance the MCD (Modified Comfortable Driving) model. A new model, MCD-S (Modified Comfortable Driving for Severe weather) is proposed. Finally, a comparative analysis of the spatio-temporal diagrams, fundamental diagrams, and speed volatility between the MCD and MCD-S models is presented. Results indicate that moderate fog decreases the density at the critical phase transition, thereby reducing traffic flow efficiency and increasing congestion. It significantly affects synchronous flow, transition from orderly to wide moving jams in the first-order phase transition. Additionally, moderate fog conditions lead to more stable vehicle following and reduced aggressive driving behavior.