With the rapid growth of power demand and the advancement of new power system intelligence, smart energy measurement system data quality and security are also facing the influence of diversified factors. To solve the series of problems such as low data prediction efficiency, poor security perception, and “data islands” of the new power system, this paper proposes a federated learning system based on the Improved Hunter–Prey Optimizer Optimized Wavelet Neural Network (IHPO-WNN) for the whole-domain power load prediction. An improved HPO algorithm based on Sine chaotic mapping, dynamic boundaries, and a parallel search mechanism is first proposed to improve the prediction and generalization ability of wavelet neural network models. Further considering the data privacy in each station area and the potential threat of cyber-attacks, a localized differential privacy-based federated learning architecture for load prediction is designed by using the above IHPO-WNN as a base model. In this paper, the actual dataset of a smart energy measurement master station is selected, and simulation experiments are carried out through MATLAB software to test and examine the performance of IHPO-WNN and the federal learning system, respectively, and the results show that the method proposed in this paper has high prediction accuracy and excellent practical performance.