A quantum-based long short-term memory (QLSTM) prediction model integrating the advantages of quantum high-dimensional mapping and classical temporal memory is proposed to address the problems of insufficient model generalization caused by limited historical samples and weak responsiveness to abrupt temporal dynamics in icing thickness prediction for overhead transmission lines. Based on measured icing monitoring data from a 220 kV transmission line in Jiande, Zhejiang Province, a standardized time-series training dataset is constructed. Classical temporal features are mapped into a high-dimensional Hilbert space, and a variational quantum circuit incorporating controlled-NOT (CNOT) entanglement gates is designed. By exploiting quantum interference to amplify subtle perturbation signals and representing nonlocal correlations among variables, the proposed model enhances its responsiveness to abrupt temporal dynamics. Comparative experiments with five benchmark models demonstrate that the QLSTM model achieves superior prediction performance on both the complete dataset and under limited historical sample conditions, effectively restraining overfitting and mitigating prediction lag under extreme weather conditions. The results demonstrate that the QLSTM model exhibits significant advantages in enhancing model generalization under limited historical sample conditions and improving responsiveness to abrupt temporal dynamics, providing a promising technical approach for icing early warning of overhead transmission lines.