For the unsupervised learning of spiking neural networks (SNNs), both excitatory and inhibitory signals with different arriving time should be connected to the artificial neurons, causing the high-hardware-cost issue for the implementation. In this work, a capacitor-less neuron based on the novel Leaky-FeFET (L-FeFET) device is proposed and experimentally demonstrated with remarkably reduced hardware cost of only two transistors and one resistor. For the first time, by exploiting the physics of directional ferroelectric polarization switching, both excitatory and inhibitory input connections can be emulated for the biomimetic neuronal dynamics in both experiments and simulations. Moreover, the neuronal stochastic behavior can be realized without additional hardware cost due to the inherent ferroelectric dynamics. Based on the proposed neuron, a bio-plausible SNN is efficiently implemented for clustering and inference tasks. Both biomimetic clustering by self-organizing map learning and high-accuracy (92%) inference by winner-take-all learning are realized. This work provides a promising highly-integrated neuron solution for brain-inspired neuromorphic computing system.