Spike-based neuromorphic hardware has great potential for low-energy brain-machine interfaces, leading to a novel paradigm for neuroprosthetics where spiking neurons in silicon read out and control activity of brain circuits. Neuromorphic processors can receive rich information about brain activity from both spikes and local field potentials (LFPs) recorded by implanted neural probes. However, it was unclear whether spiking neural networks (SNNs) implemented on such devices can effectively process that information. Here, we demonstrate that SNNs can be trained to classify whisker deflections of different amplitudes from evoked responses in a single barrel of the rat somatosensory cortex. We show that the classification performance is comparable or even superior to state-of-the-art machine learning approaches. We find that SNNs are rather insensitive to recorded signal type: both multi-unit spiking activity and LFPs yield similar results, where LFPs from cortical layers III and IV seem better suited than those of deep layers. In addition, no hand-crafted features need to be extracted from the data—multi-unit activity can directly be fed into these networks and a simple event-encoding of LFPs is sufficient for good performance. Furthermore, we find that the performance of SNNs is insensitive to the network state—their performance is similar during UP and DOWN states.