Spiking Neural Networks (SNNs), with their temporal processing capabilities and biologically plausible dynamics, offer a natural platform for unsupervised representation learning. However, current unsupervised SNNs predominantly employ shallow architectures or localized plasticity rules, limiting their ability to model long-range temporal dependencies and maintain temporal feature consistency. This results in semantically unstable representations, thereby impeding the development of deep unsupervised SNNs for large-scale temporal video data. We propose PredNext, which explicitly models temporal relationships through cross-view future Step Prediction and Clip Prediction. This plug-and-play module seamlessly integrates with diverse self-supervised objectives. We firstly establish standard benchmarks for SNN self-supervised learning on UCF101, HMDB51, and MiniKinetics, which are substantially larger than conventional DVS datasets. PredNext delivers significant performance improvements across different tasks and self-supervised methods. PredNext achieves performance comparable to ImageNet-pretrained supervised weights, through unsupervised training solely on UCF101. Additional experiments demonstrate that PredNext, distinct from forced consistency constraints, substantially improves temporal feature consistency while enhancing network generalization capabilities. This work provides a effective foundation for unsupervised deep SNNs on large-scale temporal video data.