Video analysis is a major computer vision task that has received a lot of attention in recent years. The current state-of-the-art performance for video analysis is achieved with Deep Neural Networks (DNNs) that have high computational costs and need large amounts of labeled data for training. Spiking Neural Networks (SNNs) have significantly lower computational costs (thousands of times) than regular non-spiking networks when implemented on neuromorphic hardware. They have been used for video analysis with methods like 3D Convolutional Spiking Neural Networks (3D CSNNs). However, these networks have a significantly larger number of parameters compared with spiking 2D CSNN. This, not only increases the computational costs, but also makes these networks more difficult to implement with neuromorphic hardware. In this work, we use CSNNs trained in an unsupervised manner with the Spike Timing-Dependent Plasticity (STDP) rule, and we introduce, for the first time, Spiking Separated Spatial and Temporal Convolutions (S3TCs) for the sake of reducing the number of parameters required for video analysis. This unsupervised learning has the advantage of not needing large amounts of labeled data for training. Factorizing a single spatio-temporal spiking convolution into a spatial and a temporal spiking convolution decreases the number of parameters of the network. We test our network with the KTH, Weizmann, and IXMAS datasets, and we show that S3TCs successfully extract spatio-temporal information from videos, while increasing the output spiking activity, and outperforming spiking 3D convolutions.