The low maintenance requirement, capacity scalability, and pay-as-you-go properties of cloud computing are attractive for the virtualized deployment of diverse web services. Web traffic is typically handled by multiple server mirrors that are spatially dispersed to satisfy the expectations of a large number of worldwide users. Since the energy consumption of each server depends on its workload, the use of web routing opens the possibility of reducing operational costs through the exploitation of the regional and temporal differences in energy pricing at the mirroring sites. On the downside, the shared nature of the cloud and the network brings potential latency issues that could impact the quality of service of many applications. In this paper, we report on experimental results obtained from a web service system that uses learning automata, a reinforcement learning approach to make dynamic routing decisions based on a cost and quality-of-service criteria in the cloud. The experiments were conducted using a network of 24 nodes running in the CloudLab with time-varying energy prices that were modeled from real data.