Rumor spreading plays an important role in social communications. Moreover, it forms the basis for an important class of communication protocols called gossip algorithms, which are used for large-scale information dissemination in networks. In this work, we study the dissemination time for randomized broadcast in dynamic environments, like those encountered by wireless networks with mobile nodes. Specifically, we establish order bounds for the dissemination time when the underlying network connectivity matrix changes over time. We state the results for a network that undergoes a single switching time, and then establish bounds for the case where the connectivity matrix undergoes multiple switching times. In the switching time, we include possible additions of nodes. We also investigate an example of randomized gossip in vehicular networks.