Cortical neuronal networks are known to exhibit regimes of dynamical activity characterized by periods of elevated firing (up states) separated by silent phases (down states). Here, we show that up/down dynamics may emerge spontaneously in scale-free neuronal networks, provided an optimal amount of noise acts upon all network nodes. Our conclusions are drawn from numerical simulations of networks of subthreshold integrate-and-fire neurons, connected to each other according to a scale-free topology. We study the structure of the up/down regime both in time and in terms of the node degree. We also examine whether localized random perturbations applied to specific network nodes are able to generate up/down dynamics, showing that this regime arises when noisy inputs are applied to low-degree (nonhub) network nodes, but not when they act upon network hubs.