Learning new concepts rapidly from a few examples is an open issue in spike-based machine learning. This few-shot learning imposes substantial challenges to the current learning methodologies of spiking neuron networks (SNNs) due to the lack of task-related priori knowledge. The recent learning-to-learn (L2L) approach allows SNNs to acquire priori knowledge through example-level learning and task-level optimization. However, existing L2L-based frameworks do not target the neural dynamics (i.e., neuronal and synaptic parameter changes) on different timescales. This diversity of temporal dynamics is an important attribute in spike-based learning, which facilitates the networks to rapidly acquire knowledge from very few examples and gradually integrate this knowledge. In this work, we consider the neural dynamics on various timescales and provide a multi-timescale optimization (MTSO) framework for SNNs. This framework introduces an adaptive-gated LSTM to accommodate two different timescales of neural dynamics: short-term learning and long-term evolution. Short-term learning is a fast knowledge acquisition process achieved by a novel surrogate gradient online learning (SGOL) algorithm, where the LSTM guides gradient updating of SNN on a short timescale through an adaptive learning rate and weight decay gating. The long-term evolution aims to slowly integrate acquired knowledge and form a priori, which can be achieved by optimizing the LSTM guidance process to tune SNN parameters on a long timescale. Experimental results demonstrate that the collaborative optimization of multi-timescale neural dynamics can make SNNs achieve promising performance for the few-shot learning tasks.