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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.