Future field work tasks will require mountain tractors to pass through rough terrain with limited human supervision. The wheel–soil interaction plays a critical role in rugged terrain mobility. In this paper, an algorithm for the estimation of soil characteristic parameters based on the Simpson numerical integration method and Gauss–Newton iteration method is presented. These parameters can be used for passability prediction or in a traction control algorithm to improve tractor mobility and to plan safe operation paths for autonomous navigation systems. To verify the effectiveness of the solving algorithm, different initial values and soils were selected for simulation calculations of soil characteristic parameters such as internal friction angle, settlement index, and the joint parameter of soil cohesion modulus and friction modulus. The results show that the error was kept within 2%, and the calculation time did not exceed 0.84 s, demonstrating high robustness and real-time performance. To test the applicability of the algorithm model, further research was conducted using different wheel parameters of electric mountain tractors under wet clay conditions. The results show that these parameters also have high accuracy and stability with only a few iterations. Thus, the estimation algorithm can meet the requirements of quickly and accurately identifying soil characteristic parameters during tractor operation. A criterion for the passability of wheeled tractors through unknown terrain is proposed, utilizing identified soil parameters.