Drone delivery has garnered significant attention recently due to its potential for faster delivery at lower cost relative to other delivery options. When scheduling drones from a depot for delivery to various destinations, the dispatcher must take into account the uncertain wind conditions, which affect the delivery times of drones to their destinations. To mitigate the risk of delivery delays caused by wind uncertainty, we propose a two- period drone scheduling model to robustly optimize the delivery schedule. In this framework, the scheduling decisions are made in the morning, with provision for different delivery schedules in the afternoon that adapt to updated weather information available by midday. Our approach minimizes the essential riskiness index (Zhang et al. 2019), which can limit the probability of tardy delivery and the magnitude of lateness. Using wind observation data, we characterize the uncertain flight times via a cluster-wise ambiguity set, which has the benefit of tractability while avoiding overfitting to the empirical distribution. The cluster-wise ambiguity set enables us to adapt the intraday delivery schedule depending on which cluster on the wind vector chart the observed morning wind vector belongs to. A branch-and-cut algorithm is developed to solve the adaptive distributionally robust optimization model.