Traditional task offloading strategies in edge computing often rely on static heuristics or data-intensive machine learning models, which are not always suitable for highly dynamic and resource-constrained environments. In this paper, we propose a novel task-offloading framework based on Spiking Neural Networks inspired by the efficiency and adaptability of biological neural systems. Our approach integrates an SNN-based decision module into edge nodes to perform real-time, energy-efficient task orchestration. We evaluate the model under various IoT workload scenarios using a hybrid simulation environment composed of YAFS and Brian2. The results demonstrate that our SNN-based framework significantly reduces task processing latency and energy consumption while improving task success rates. Compared to traditional heuristic and ML-based strategies, our model achieves up to 26% lower latency, 32% less energy consumption, and 25\% higher success rate under high-load conditions.