In wireless sensor networks deployed for collecting data related to environmental monitoring a challenging issue is to distribute relaying traffic evenly among the networks nodes to avoid overloads with consequent fast battery depletion of nodes located near base stations. In this paper we address the issue by considering the use of mobile base stations and energy-aware multi-hop geographic forwarding of data packets. Geographic forwarding is able to adaptively build a route for each packet in a dynamic scenario where base stations move, channel fluctuates due to fading, and sensor nodes periodically sleep and wake up to spare energy. More precisely, here we provide a model for offline estimation of traffic load distribution in the network when single/multiple base station move along a trajectory. Moreover, we propose and investigate forwarding strategies which try to trade off energy-efficiency of single packet collection with overload balancing among relays.