Federated learning combined with Spiking Neural Networks (SNNs) provides a reliable and lightweight solution for privacy and energy constraints in billions of edge devices. However, the current rate-coding in SNNs has high latency and leads to increased power consumption. In this study, we develop a federated neuromorphic learning (FNL) system based on temporal coding to process edge information quickly and efficiently using compact neurons with time-to-first spike (TTFS) coding. These neurons are demonstrated using the volatile threshold switching characteristics of VO2 memristors. We implemented an FNL system for edge pattern recognition in hardware using these compact neurons. Notably, the memristor-based edge device with TTFS-coding shows 330× and 76× improvements in interference speed and energy consumption, respectively, compared to the conventional rate-coding scheme. Furthermore, a multimodal FNL system with TTFS-coding is demonstrated to process audio-visual vehicle signals from edge traffic scenes, with spike numbers for each iteration of edge devices being 26× lower compared to the rate-coding scheme. Our system, incorporating FNL and TTFS-coding, can facilitate the development of next-generation edge artificial intelligence requiring extremely low latency and power.