The prediction in the design phase of the stability of ground vehicles subject to transient crosswinds become of increased concern with drag reduced shapes, lighter vehicles as well as platooning. The objective of this work is to assess the order of model complexity needed in numerical simulations to capture the behavior of a ground vehicle passing through a transient crosswind. The performance of a full-dynamic coupling between aerodynamic and vehicle dynamic simulations, including a driver model, is evaluated. In the simulations a feedback from the vehicle dynamics into the aerodynamic simulation is performed in every time step. In the work, both the vehicle dynamic response and the aerodynamic forces and moments are studied. The results are compared to a static coupling approach on a set of different vehicle geometries. Five car-type geometries and one simplified bus geometry are evaluated. The aerodynamic loads and moments are obtained using Detached Eddy Simulation (DES) where the motion of the vehicle is enabled using an overset mesh technique. This motion is calculated with a single-track model, including a driver model and handling two degrees of freedom, namely lateral translation and yaw motion.The results show that for vehicles undertaking large yaw moments and therefore large yaw motions, like the bus-type geometry, the full dynamic coupling is beneficial. In this case, a static coupling overestimates the aerodynamic loads and in turn the vehicle motion. On less crosswind sensitive vehicles, like the car-type geometries, the full-coupling approach does not modify the results in a significant way compared to a static coupling.