Skid-Steer Wheeled Mobile Robots (SSWMRs) are increasingly being used for off-road autonomy applications. When turning at high speeds, these robots tend to undergo significant skidding and slipping. In this work, using Gaussian Process Regression (GPR) and Sigma-Point Transforms, we estimate the non-linear effects of tire-terrain interaction on robot velocities in a probabilistic fashion. Using the mean estimates from GPR, we propose a data-driven dynamic motion model that is more accurate at predicting future robot poses than conventional kinematic motion models. By efficiently solving a convex optimization problem based on the history of past robot motion, the GPR augmented motion model generalizes to previously unseen terrain conditions. The output distribution from the proposed motion model can be used for local motion planning approaches, such as stochastic model predictive control, leveraging model uncertainty to make safe decisions. We validate our work on a benchmark real-world multi-terrain SSWMR dataset. Our results show that the model generalizes to three different terrains while significantly reducing errors in linear and angular motion predictions. As shown in the attached video, we perform a separate set of experiments on a physical robot to demonstrate the robustness of the proposed algorithm.