This paper addresses the data-aided signal-to-noise ratio (SNR) estimation in time-variant flat Rayleigh fading channels. The time-variant fading channel is modeled by considering the Jakes' model and the first order autoregressive (ARl) model. Closed-form expressions of the Cramer-Rao bound (CRB) for data-aided SNR estimation are derived for fast and slow fading Rayleigh channels. As a special case, the CRB under uncorrelated fading Rayleigh channel is derived. Analytical approximate expressions of the CRB are derived for low and high SNR that enable the derivation of a number of properties that describe the bound's dependence on key parameters such as SNR, channel correlation, sample number. Since the exact maximum likelihood (ML) estimator is computationally intensive in the case of fast-fading channel, two approximate solutions are proposed for high and low SNR cases. Numerical results illustrate the performance of the estimators and confirm the validity of the theoretical analysis.