This paper tackles a Bayesian Decision Making approach for unmanned aerial vehicle (UAV) mission that allows UAV to quickly react to unexpected events under dynamic environments. From online observations and the mission statement, the proposed approach is designed by means of Dynamic Bayesian Networks (DBN) arising from the safety or performance failures analysis. After proposing a DBN model, a probabilistic approach based on Multiple-Criteria Decision-Making (MCDM) is then applied to find the best configuration reaching a balance between performance and energy consumption, thus decide which tasks will be implemented as SW and which as HW execution units, regarding the mission requirement. The proposal UAV mission decision-making is three-pronged, providing: (1) real time image pre-processing of sensor observations; (2) temporal and probabilistic approach based on Bayesian Networks to continuously update the mission plan during the flight; and (3) low-power hardware and software implementations for online and real time embedded Decision Making using Xilinx System on Programmable Chip (SoPC) platform. The proposed approach is then validated with a practical case UAV mission planning using the proposed dynamic decision-maker implemented on embedded system based on a hybrid device.