The neural sampling core (NSC) proposed herein offers a spintronic device-based circuit and learning mechanism utilizing imprecise and stochastic components, similar to biological brains, to realize ultralow-power neuromorphic computations at subthreshold voltages. Leveraging principles from neural sampling, a biologically plausible theory from computational neuroscience, a spintronic stochastic spiking neuron with digital Postsynaptic potentials is proposed in conjunction with low-precision spintronic synapses utilizing a new event-driven Probabilistic Hebbian Plasticity Rule, and a novel homeostasis mechanism that balances neural activity across multiple timescales and process variation effects. The primary computational operation, the summation of presynaptic potentials weighted by their corresponding synaptic efficacy and the neuron's homeostatic parameters, is performed in a parallel analog fashion using noisy and imprecise subthreshold components. It is demonstrated herein that the NSC is capable of learning orientation selectivity, much like the simple cells found in the visual cortex, in an unsupervised fashion at 311 nW per neuron and 1.9-7.7 nW per active synapse using a 200-mV supply voltage.