Predicting the response parameters of ice-covered overhead transmission lines (OHTLs) is critical for assessing the reliability of power systems. However, current methodologies face significant challenges: physics-based simulations are computationally demanding and thus infeasible for real-time applications, while conventional machine learning (ML) models often lack generalization capability due to the absence of physical constraints. To address these challenges, this article proposes a novel physics-augmented machine learning (PAML) model, which integrates underlying physical mechanisms into the mapping from inputs to outputs. Specifically, we construct a high-quality hybrid dataset by augmenting limited measured data with high-fidelity simulated data. Building on the augmented dataset, a hybrid-effects regression architecture is devised to capture the complex variability of icing response across different scenarios. Furthermore, a two-stage screening workflow is proposed to select effective ML algorithms from a comprehensive pool of candidates, and an adaptive weighting mechanism is then developed to achieve their optimal integration. Results indicate that the PAML model significantly reduces computational overhead while maintaining high accuracy. Notably, it demonstrates superior generalization across unseen scenarios, outperforming conventional ML approaches.