Cooperative path planning for unmanned aerial vehicle (UAV) swarms has attracted considerable research attention, yet it remains challenging in complex, uncertain environments. To tackle this problem, we model the cooperative path planning task as a heterogeneous decentralized Markov Decision Process (MDP), emphasizing the symmetry-inspired role assignment between leader and wingmen UAVs, which ensures balanced and coordinated behaviors in dynamic settings. We address the problem using a Multi-Agent Soft Actor-Critic (MASAC) framework enhanced with a symmetry-aware reward mechanism designed to optimize multiple cooperative objectives: simultaneous arrival, formation topology preservation, dynamic obstacle avoidance, trajectory smoothness, and inter-agent collision avoidance. This design promotes behavioral symmetry among agents, enhancing both coordination efficiency and system robustness. Simulation results demonstrate that our method achieves efficient swarm coordination and reliable obstacle avoidance. Quantitative evaluations show that our MASAC-CA algorithm achieves a Mission Success Rate (MSR) of 99.0% with 2–5 wingmen, representing approximately 13% improvement over baseline MASAC, while maintaining Formation Keeping Rates (FKR) of 59.68–26.29% across different swarm sizes. The method also reduces collisions to near zero in cluttered environments while keeping flight duration, path length, and energy consumption at levels comparable to baseline algorithms. Finally, the proposed model’s robustness and effectiveness are validated in complex uncertain environments, underscoring the value of symmetry principles in multi-agent system design.