Smart microgrid energy management requires accurate energy forecasting and robust scheduling strategies. However, comprehensive uncertainty quantification in stochastic load scheduling remains limited. This study conducts an in-depth evaluation of uncertainty-aware load scheduling for building cooling systems integrated with thermal energy storage (TES). Firstly, a virtual simulation platform for an office building energy system was developed based on a TRNSYS. Secondly, Uncertainty in scheduling inputs—such as chilled water supply temperature, weather forecasts, and thermal load—was characterized based on their statistical patterns and temporal dynamics. These uncertainties were propagated through energy forecasting models to derive the most probable energy consumption scenarios. Finally, we proposed a generic stochastic scheduling framework that utilizes the probabilistic energy forecast to optimize TES operations. Results show that TES improves system operational efficiency by enabling strategic chiller turn-off and avoiding inefficient partial load operation during both charging and discharging phases. With the proposed uncertainty-informed scheduling strategy, the electricity cost is reduced by 9.2%. This confirms that integrating uncertainty quantification into energy forecasting and scheduling can yield significant economic and operational benefits for building cooling systems equipped with TES.