In this paper, we consider a compressive sleeping wireless sensor network (WSN) for monitoring parameters in the sensor field, where only a fraction of sensor nodes (SNs) are activated to perform the sensing task and their data are gathered at a fusion center (FC) to estimate all the other SNs’ data using the compressive sensing (CS) principle. Typically, research published concerning CS implicitly assume the sampling costs for all samples are equal and suggest random sampling as an appropriate approach to achieve good reconstruction accuracy. However, this assumption does not hold for compressive sleeping WSNs, which have significant variability in sampling cost owing to the different physical conditions at particular SNs. To exploit this sampling cost nonuniformity, we propose a cost-aware activity scheduling approach that minimizes the sampling cost with constraints on the regularized mutual coherence of the equivalent sensing matrix. In addition, for the case with prior information about the signal support, we extend the proposed approach to incorporate the prior information by considering an additional constraint on the mean square error (MSE) of the oracle estimator for sparse recovery. Our numerical experiments demonstrate that, in comparison with other designs in the literature, the proposed activity scheduling approaches lead to improved tradeoffs between reconstruction accuracy and sampling cost for compressive sleeping WSNs.