This paper proposes a novel method to estimate the wheel dynamic load based on the gas pressure of a hydro-pneumatic suspension. A nonlinear coupled model between suspension chamber pressure and tire-ground contact force is developed, integrating suspension dynamics with its nonlinear stiffness characteristics. An iterative algorithm is developed to estimate wheel dynamic load using data from only one single pressure sensor, thereby eliminating the reliance on traditional tire models and complex multi-sensor fusion frameworks. This method effectively reduces hardware redundancy and minimizes the propagation of measurement errors. The proposed model is experimentally validated on a dedicated suspension test bench, demonstrating satisfactory agreement between the measured and estimated data. Additionally, co-simulation with TruckSim verifies the accuracy of both the calculated damping force and wheel dynamic load, demonstrating the effectiveness of the model on characterizing the mechanical behavior of the hydro-pneumatic suspension system. The proposed method provides a practical, low-cost, and efficient solution with minimal hardware dependencies.