With the implementation of the green development strategy and the “double carbon goal”, as an important energy for sustainable development, wind power has been widely researched and vigorously developed across the world. Wind speed prediction has a major impact on the grid dispatching of wind power connection. Most current studies only focus on the deterministic prediction of wind speed. However, the traditional deterministic forecast only provides the single wind speed prediction results and cannot meet the diverse demands of dispatchers. To bridge the gap, a wind speed point-interval forecasting method is proposed that utilizes empirical wavelet transform, an improved wild horse optimization algorithm, a multi-predictor, and improved kernel density estimation. This method decomposes the wind speed sequence into stationary subsequences through empirical wavelet transform, and then optimizes three basic learners with completely different learning mechanisms to form an ensemble model using the modified wild horse optimization algorithm. Finally, the uncertainty is analysed using an improved kernel density estimation. The datasets of three sites from America’s national renewable energy laboratory are used for comparison experiments with other models, and the predictions are discussed from different angles. The simulation results demonstrate that the model can produce high-precision deterministic results and high-quality probabilistic results. The reference information the model provides can be extremely valuable for scheduling operators.