Electrowetting (EW) is a powerful tool to control fluid motion at the microscale and has promising applications in the field of microfluidics. The present work analyzes the influence of an electrowetting voltage in determining and altering the state of a static droplet resting on a rough surface. An energy-minimization-based modeling approach is used to analyze the influence of interfacial energies, surface roughness parameters, and electric fields in determining the apparent contact angle of a droplet in the Cassie and Wenzel states under the influence of an EW voltage. The energy-minimization-based approach is also used to analyze the Cassie-Wenzel transition under the influence of an EW voltage and estimate the energy barrier to transition. The results obtained show that EW is a powerful tool to alter the relative stabilities of the Cassie and Wenzel states and enable dynamic control of droplet morphology on rough surfaces. The versatility and generalized nature of the present modeling approach is highlighted by application to the prediction of the contact angle of a droplet on an electrowetted rough surface consisting of a dielectric layer of nonuniform thickness.