We propose a methodology based on reservoir computing for mapping local proprioceptive information acquired at the level of the leg joints of a simulated quadruped robot into exteroceptive and global information, including both the ground reaction forces at the level of the different legs and information about the type of terrain traversed by the robot. Both dynamic estimation and terrain classification can be achieved concurrently with the same reservoir computing structure, which serves as a soft sensor device. Simulation results are presented together with preliminary experiments on a real quadruped robot. They demonstrate the suitability of the proposed approach for various terrains and sensory system fault conditions. The strategy, which belongs to the class of data-driven models, is independent of the robotic mechanical design and can easily be generalized to different robotic structures.