Fog typically results in reduced atmospheric visibility. Severely limited visibility has a significant impact on transportation, particularly the operations of aircraft. Precise forecasts of low visibility are essential for aviation services, primarily for the efficient planning of airport activities. Despite the utilization of sophisticated numerical weather prediction (NWP) models, the prediction of fog and limited visibility remains challenging. The intricacy of fog prediction is due to limitations in understanding the micro-scale factors that lead to fog genesis, intensification, persistence, and dissipation. This study investigates the occurrence of fog (surface visibility <1000 m) and dense fog (surface visibility < 200 m) throughout the climatological low-visibility months (November to February) to analyze the persistence of low-visibility events and predict them in the specific conditions of the frog prone Indo-Gangetic Plain (IGP) regions. A representative station, Jay Prakash Narayan International (JPNI) Airport in Patna, India, has been considered given the availability of instrumental quality datasets. The analysis investigates the long-term and short-term persistence and prediction of the series using a diverse variety of machine learning (ML) algorithms. To conduct a comprehensive analysis over an extended period, detrended fluctuation analysis (DFA) is employed to determine the similarities between the time series of large-scale fog and dense fog. A Markov chain model is used to look at the binary time series and figure out how long low-visibility events (like fog and dense fog) last in the short term ( 1-5 hours). Ultimately, we analyze a short-term forecast (Nowcast) with a lead time of one to five hours for instances of low visibility (fog or dense fog). This nowcasting is generated utilizing diverse methodologies, including Markov chain models, persistence analysis, and machine learning (ML) methods. Finally, establish that the most favorable and reliable results in this prediction problem are attained by employing a Mixture of Experts model that integrates persistence-based methods and ML algorithms.