Despite recent progress in training spiking neural networks (SNNs) for classification, their application to continuous motor control remains limited. Here, we demonstrate that fully spiking architectures can be trained end-to-end to control robotic arms with multiple degrees of freedom in continuous environments. Our predictive-control framework combines Leaky Integrate-and-Fire dynamics with surrogate gradients, jointly optimizing a forward model for dynamics prediction and a policy network for goal-directed action. We evaluate this approach on both a planar 2D reaching task and a simulated 6-DOF Franka Emika Panda robot with torque control. In direct comparison to non-spiking recurrent baselines trained under the same predictive-control pipeline, the proposed SNN achieves comparable task performance while using substantially fewer parameters. An extensive ablation study highlights the role of initialization, learnable time constants, adaptive thresholds, and latent-space compression as key contributors to stable training and effective control. Together, these findings establish spiking neural networks as a viable and scalable substrate for high-dimensional continuous control, while emphasizing the importance of principled architectural and training design.