We investigate a remote estimation problem in which a transmitter observes a Markov source and chooses the power level to transmit it over a time-varying packet-drop channel. The channel is modeled as a channel with Markovian state where the packet drop probability depends on the channel state and the transmit power. A receiver observes the channel output and the channel state and estimates the source realization. The receiver also feeds back the channel state and an acknowledgment for successful reception to the transmitter. We consider two models for the source-finite state Markov chains and first-order autoregressive processes. For the first model, using ideas from team theory, we establish the structure of optimal transmission and estimation strategies and identify a dynamic program to determine optimal strategies with that structure. For the second model, we assume that the noise process has unimodal and symmetric distribution. Using ideas from majorization theory, we show that the optimal transmission strategy is symmetric and monotonic and the optimal estimation strategy is like Kalman filter. Consequently, when there are a finite number of power levels, the optimal transmission strategy may be described using thresholds that depend on the channel state. Finally, we propose a simulation-based approach (renewal Monte Carlo) to compute the optimal thresholds and optimal performance and elucidate the algorithm with an example.