Highly Automated Vehicles (HAVs) are expected to improve the performance of terrestrial transportations by providing safe and efficient travel experience to drivers and passengers. As HAVs will be equipped with different driving automation levels, they should be capable to dynamically adapt their Level of Autonomy (LoA), in order to tackle sudden and recurrent changes in their environment (i.e., inclement weather, complex terrain, unexpected on-road obstacles, etc.). In this respect, HAVs should be able to respond not only on causal reasoning effects, which depend on present and past inputs from the external driving environment, but also on non-causal reasoning situations depending on future states associated with the external driving scene. On the other hand, driver’s personal preferences and profile characteristics should be assessed and managed properly, in order to enhance travel experience. In the light of the above, the present paper aims to tackle these challenges on how cognitive computing enables HAVs to operate each time in the best available LoA by responding quickly to changing environment situations and driver’s preferences. On this basis, an in-vehicle cognitive functionality is introduced, which collects data from various sources (sensor and driver layers), intelligently processing it to the decision-making layer, and finally, selecting the optimal LoA by integrating previous knowledge and experience. The overall approach includes the identification and utilization of a hybrid (data-driven and event-driven) algorithmic process towards reaching intelligent and proactive decisions. An indicative discrete event simulation analysis showcases the efficiency of the developed approach in proactively adapting the vehicle’s LoA.