Accurate short-term wind power forecasting plays a critical role in maintaining grid stability due to the inherently irregular and fluctuating nature of wind resources. Deep learning models such as LSTM, GRU, and CNN are widely used to learn temporal dynamics; however, their ability to capture or adapt to the underlying symmetries and asymmetries inherent in real-world wind energy data remains insufficiently explored. In this study, we evaluate and compare these models using authentic production and meteorological data from the Tokat Wind Farm in Türkiye. The forecasting scenarios were designed to reflect the temporal structure of the dataset, including seasonal patterns, recurrent behaviors, and the symmetry-breaking effects caused by abrupt changes in wind speed and operational variability. The results demonstrate that the LSTM model most effectively captures the temporal relationships and partial symmetries within the data, yielding the lowest error metrics (RMSE = 0.2355, MAE = 0.1249, MAPE = 25.16%, R² = 0.8199). GRU and CNN offer moderate performance but show reduced sensitivity to asymmetric fluctuations, particularly during periods of high variability. The comparative findings highlight how symmetry-informed model behavior—specifically the ability to learn repeating temporal structures and respond to symmetry-breaking events—can significantly influence forecasting accuracy. This study provides practical insights into the interplay between data symmetries and model performance, supporting the development of more robust deep learning approaches for real-world wind energy forecasting.