This paper focuses on the differential privacy fusion filtering problem for multi-rate nonlinear systems over sensor networks based on signal-to-noise ratio (SNR), in which a compensation strategy with a single exponential smoothing method is employed to handle the multiple time series stemmed from the multi-rate sampling strategy. Considering the inherent vulnerabilities of the SNR-based sensor networks, packet dropouts and eavesdropping attacks may occur during the measurement transmission between adjacent nodes, where the probability of packet dropouts varies with the SNR. In order to prevent potential eavesdroppers from inferring system states through measurement signals and causing sensitive information leakage, the transmitted measurement signals are disturbed with random noises. On this basis, the differential privacy is introduced as a performance metric to evaluate the protection level, and the perturbation noises are designed with the help of privacy parameters and measurement matrices. Firstly, a second-order center difference approach is exploited to deal with the nonlinear function. Subsequently, the upper bound on the local filtering error covariance is obtained by solving the matrix difference equation, and the local filtering algorithm is designed by minimizing the upper bound. Then, the federated fusion criterion is utilized to further improve the estimation accuracy of local filters, and the filtering performance is analyzed from the perspective of monotonicity. Finally, the effectiveness of the algorithm is illustrated through the simulation of induction machines with comparative experiments.