Climate-driven variations in rainfall, infiltration, and temperature substantially alter matric suction and the hydro-mechanical response of geosynthetic-reinforced pile-supported (GRPS) embankments, yet no existing analytical model explicitly captures these coupled effects. This study first develops a climate-responsive hydro-mechanical framework that integrates an unsaturated soil arching formulation and a soil–geosynthetic interaction model into a single analytical framework for GRPS embankments. A new climate–suction interaction index is introduced to capture how seasonal hydraulic forcing alters suction and, in turn, governs load transfer and system stability. Closed-form solutions integrating suction-dependent strength and stiffness are derived for arching efficacy, stress concentration ratio, geosynthetic tensile force, and differential settlement under transient climatic conditions. The framework is further extended to incorporate temperature effects through a temperature-dependent matric suction formulation, enabling the model to account for thermal-hydro-mechanical influences on soil strength and stiffness. Validation against full-scale field measurement shows excellent agreement between theoretical predictions and observed load redistribution, reinforcement tension, and deformation. The results indicate that rainfall infiltration weakens soil arching and increases reinforcement demand, while evaporation-driven drying and lower temperatures enhance suction, stiffen the soil skeleton, and improve load-transfer efficiency. The proposed framework provides a physically consistent and computationally efficient analytical tool for climate-responsive design of GRPS embankments, bridging the gap between simplified analytical approaches and computationally intensive numerical simulations.