The transition to sustainable Open Radio Access Network (O-RAN) architectures brings new challenges for resource management, especially in predicting the utilization of Physical Resource Block (PRB)s. In this paper, we propose a novel approach to characterize the PRB load using probabilistic forecasting techniques. First, we provide background information on the O-RAN architecture and components and emphasize the importance of energy/power consumption models for sustainable implementations. The problem statement highlights the need for accurate PRB load prediction to optimize resource allocation and power efficiency. We then investigate probabilistic forecasting techniques, including Simple-Feed-Forward (SFF), DeepAR, and Transformers, and discuss their likelihood model assumptions. The simulation results show that DeepAR estimators predict the PRBs with less uncertainty and effectively capture the temporal dependencies in the dataset compared to SFF- and Transformer-based models, leading to power savings. Different percentile selections can also increase power savings, but at the cost of over-/under provisioning. At the same time, the performance of the Long-Short Term Memory (LSTM) is shown to be inferior to the probabilistic estimators with respect to all error metrics. Finally, we outline the importance of probabilistic, prediction-based characterization for sustainable O-RAN implementations and highlight avenues for future research.