In recent years, wind power has emerged as an important source of renewable energy. When onshore and offshore wind farm regions are connected to the grid for power generation, consistent multi-location short-term wind power predictions are extremely valuable in terms of assuring the power system's safety, sustainability, and economic operation. An abrupt variation in wind power generation influences the efficiency of the regional power grid. This makes accurate short-term forecasting essential for high-level planning and scheduling of power grids. To address the issue, this paper presents two variants of recurrent neural networks (RNN): gated recurrent unit (GRU) and long short-term memory (LSTM) models considering substantially better prediction accuracy to forecast a country-wide (Germany) wind power data for daily (t + 1), and multi-step (t + 3, t + 5, and t + 12) hours ahead. In addition, wind velocities [m/s] measured at heights of 2, 10, and 50-m (above ground level) are exploited as an essential characteristic among the available input variables and evaluated each feature subset based on four training divisions (80-20%, 70-30%, 60-40%, and 50-50%) and compared the results with ARIMA and SVR approaches in the literature. The findings reveal that the RNN-GRU model not only can achieve higher predicting accuracy but also has a faster learning speed over long sequences.