Crop yield distribution modeling faces three key challenges: complex distributional structure, limited historical data at the county level, and the need to incorporate evolving climate conditions into distributional dynamics. We propose a Fixed-Effect Panel Neural Mixture (FEPNM) framework to address these challenges. FEPNM extends finite mixture models to a panel data setting, allowing information sharing across counties through fixed effects to mitigate short time-series limitations. We further generalize the mixture model into a Mixture-of-Experts (MoE) type specification by introducing a neural-network gating mechanism that flexibly maps climate variables and conservation practices to time-varying regime probabilities. This structure enables direct modeling of the probability of yield loss as a nonlinear function of climate exposure and management adoption. Simulations demonstrate that FEPNM substantially improves the precision of structural parameter estimates and average partial effects, particularly in short-T settings. In an empirical application to U.S. county-level corn yields, FEPNM outperforms conventional mixture and single-distribution specifications in both in-sample and out-of-sample likelihood. Our results provide structural evidence on how climate exposure and conservation practices jointly shape corn yield distributions. Heating Degree Days (HDD) significantly increase the probability of yield loss, while adoption of cover crops and no-tillage practices significantly reduces downside yield risk. These findings highlight the importance of incorporating nonlinear climate effects and management practices into distributional modeling for agricultural risk management and crop insurance design.