We characterize wrinkling on the surfaces of prestrained polystyrene sheets coated with thin polytetrafluoroethylene skins using a combination of mechanical strain measurements and 3D finite element simulations. The simulations show that wrinkle wavelength increases with skin thickness, in agreement with a well-known continuum model and recent experiments. The wrinkle amplitudes also increase with strain. Nanoinclusions, such as holes and patterned lines, influence wrinkle patterns over limited distances, and these distances are shown to scale with the wrinkle wavelengths. Good agreement between experimental and simulated influence distances is observed. The inclusions provide strain relief, and they behave as if they are attracting adjacent material when the sheets are under strain. The wrinkles have stiffnesses in much the same way as do polymers (but at different length scales), a property that is quantified for polymers using persistence lengths. We show that the concept of persistence length can be useful in characterizing the wrinkle properties that we have observed. However, the calculated persistence lengths do not vary systematically with thickness and strain, as interactions between neighboring wrinkles produce confinement that is analogous to the kinetic confinement of polymers.