Heavy vehicles exiting (or entering) a tunnel at high speed under a strong crosswind is a particularly critical condition since the aerodynamic load changes drastically, greatly affecting the lateral stability of the vehicle. Often, active control systems (active suspensions, active front steering, etc.) and infrastructure elements (e.g., wind fences) are proposed to reduce the induced risks. To help the design of these devices, the present paper investigates the response of the vehicle–driver system in the case of a high-sided lorry exiting a tunnel under crosswind, by using Driver-In-the-Loop simulations. The study was performed using the dynamic driving simulator of Politecnico di Milano and 28 test drivers. Vehicle and aerodynamic models have been developed to reproduce the phenomenon in a highly immersive environment. During the tests, several combinations of vehicle and wind speed were considered. The effect of vehicle loading condition (Empty and Laden) was also investigated. The performed tests allowed us to gain information about the sequence of the driver’s actions and associated delays, which may induce lane deviation or, in the worst case, rollover. It was found that lane invasion may happen for ratios of lateral aerodynamic force over vehicle weight force bigger than 0.1, while rollover could happen for ratios bigger than 0.3. Moreover, it was found that the driver’s response typically happens with a delay of ∼0.25 s with respect to the onset of the crosswind stimulus.