The wetting configuration of a liquid droplet on a rough or physically patterned surface is typically characterized by either the Cassie wetting mode, in which the droplet resides on top of the roughness, or the Wenzel mode, in which the droplet penetrates into the roughness. For a fixed surface topology and droplet size, one of these modes corresponds to the global free-energy minimum. However, the other state is often metastable and long-lived due to a free-energy barrier that hinders the transition between the two wetting states. Metastable wetting states have been observed experimentally, and we also observe them in molecular dynamics (MD) simulations of a droplet on a grooved surface. Using forward flux sampling, we study the kinetics of the Cassie to Wenzel and Wenzel to Cassie transitions for two-dimensional droplets on periodically grooved substrates. The global-minimum wetting states that emerge from our nanoscale MD approach are consistent with those predicted by a macroscopic model based on free energy minimization. We find that the free-energy barriers for these transitions depend on the droplet size and surface topology. A committor analysis indicates that the transition-state ensemble consists of droplets that are on the verge of initiating/breaking contact with the substrate at the bottom of the grooves.