Many authors have reported the use of deep learning techniques to model wind power forecasts. For shorter-term prediction horizons, the training and deployment of such models is hindered by their computational cost. Neuromorphic computing provides a new paradigm to overcome this barrier through the development of devices suited for applications where latency and low-energy consumption play a key role, as is the case in real-time short-term wind power forecasting. The use of biologically inspired algorithms adapted to the architecture of neuromorphic devices, such as spiking neural networks, is essential to maximize their potential. In this paper, we propose a short-term wind power forecasting model based on spiking neural networks adapted to the computational abilities of Loihi, a neuromorphic device developed by Intel. A case study is presented with real wind power generation data from Ireland to evaluate the ability of the proposed approach, reaching a normalised mean absolute error of 2.84 percent for one-step-ahead wind power forecasts. The study illustrates the plausibility of the development of neuromorphic devices aligned with the specific demands of the wind energy sector.