Intuitive and easily comprehensible interaction is crucial for the development of augmented reality (AR) applications. To design interaction methods and metaphors that can dynamically adapt to individual users, it is essential to consider their cognitive requirements. This paper investigates the feasibility of using gaze tracking as a means of assessing the cognitive load of interactions in AR environments and explores whether real-time predictions can enable continuous adaptation of the application to the mental states of users. In a user study involving 22 participants, gaze data was collected using the HoloLens 2 while participants completed search tasks of varying difficulty within an AR setting. Analysis revealed significant differences in gaze behavior corresponding to task difficulty. Based on the collected data, two machine learning models were trained to classify cognitive load levels using a sliding-window approach. The models achieved classification accuracies ranging from 50% to 80%, demonstrating the potential of gaze-based cognitive load estimation for real-time adaptation in AR applications.