Spiking Neural Networks (SNNs) are promising candidates for low-power edge computing in domains such as wearable sensing and time-series analysis. A key neuronal parameter, the leaky time constant (LTC), governs temporal integration of information in Leaky Integrateand-Fire (LIF) neurons, yet its impact on feedforward SNN performance across different data modalities remains underexplored. This study investigates the role of LTC in a temporally adaptive feedforward SNN applied to static image, dynamic image, and biosignal time-series classification. Presented experiments demonstrate that LTCs critically affect inference accuracy, synaptic weight distributions, and firing dynamics. For static and dynamic images, intermediate LTCs yield higher accuracy and compact, centered weight histograms, reflecting stable feature encoding. In time-series tasks, optimal LTCs enhance temporal feature retention and result in broader weight sparsity, allowing for tolerance of LTC variations. The provided results show that inference accuracy peaks at specific LTC ranges, with significant degradation beyond this optimal band due to over-integration or excessive forgetting. Firing rate analysis reveals a strong interplay between LTC, network depth, and energy efficiency, underscoring the importance of balanced spiking activity. These findings reveal that task-specific LTC tuning is essential for efficient spike coding and robust learning. The results provide practical guidelines for hardware-aware SNN optimization and highlight how neuronal time constants can be designed to match task dynamics. This work contributes toward scalable, ultra-lowpower SNN deployment for real-time classification tasks in neuromorphic computing.