Agricultural management, with a particular focus on fertilization strategies, holds a central role in shaping crop yield, economic profitability, and environmental sustainability. While conventional guidelines offer valuable insights, their efficacy diminishes when confronted with extreme weather conditions, such as heatwaves and droughts. In this study, we introduce an innovative framework that integrates Deep Reinforcement Learning (DRL) with Recurrent Neural Networks (RNNs). Leveraging the Gym-DSSAT simulator, we train an intelligent agent to master optimal nitrogen fertilization management. Through a series of simulation experiments conducted on corn crops in Iowa, we compare Partially Observable Markov Decision Process (POMDP) models with Markov Decision Process (MDP) models. Our research underscores the advantages of utilizing sequential observations in developing more efficient nitrogen input policies. Additionally, we explore the impact of climate variability, particularly during extreme weather events, on agricultural outcomes and management. Our findings demonstrate the adaptability of fertilization policies to varying climate conditions. Notably, a fixed policy exhibits resilience in the face of minor climate fluctuations, leading to commendable corn yields, cost-effectiveness, and environmental conservation. However, our study illuminates the need for agent retraining to acquire new optimal policies under extreme weather events. This research charts a promising course toward adaptable fertilization strategies that can seamlessly align with dynamic climate scenarios, ultimately contributing to the optimization of crop management practices.