This paper explores the promising interplay between spiking neural networks (SNNs) and event-based cameras for privacy-preserving human action recognition (HAR). The unique feature of event cameras in capturing only the outlines of motion, combined with SNNs' proficiency in processing spatiotemporal data through spikes, establishes a highly synergistic compatibility for event-based HAR. Previous studies, however, have been limited by SNNs' ability to process long-term temporal information, essential for precise HAR. In this paper, we introduce two novel frameworks to address this: temporal segment-based SNN (\textit{TS-SNN}) and 3D convolutional SNN (\textit{3D-SNN}). The \textit{TS-SNN} extracts long-term temporal information by dividing actions into shorter segments, while the \textit{3D-SNN} replaces 2D spatial elements with 3D components to facilitate the transmission of temporal information. To promote further research in event-based HAR, we create a dataset, \textit{FallingDetection-CeleX}, collected using the high-resolution CeleX-V event camera $(1280 \times 800)$, comprising 7 distinct actions. Extensive experimental results show that our proposed frameworks surpass state-of-the-art SNN methods on our newly collected dataset and three other neuromorphic datasets, showcasing their effectiveness in handling long-range temporal information for event-based HAR.