We experimentally and theoretically examine the influence of a double-chain cationic surfactant, didodecyldimethylammonium bromide (DDAB), on the wetting states and contact angles on superhydrophobic (SH) surfaces made of hydrophobic microcylinders. We use two types of micropatterns of different surface roughness, r, and packing fraction, phi, and vary nine dimensionless surfactant concentrations (C-S), normalized by the critical micelle concentration (CMC), in the experiments. At low C-S, some of the surfactant-laden droplets are in a gas-trapping, Cassie-Baxter (CB) state on the high-roughness microstructures. In contrast, some droplets are in a complete-wetting Wenzel (W) state on the low-roughness microtextures. We found that the contact angle of CB drops can be well predicted using a thermodynamic model considering surfactant adsorption at the liquid-vapor (LV) and solid-liquid (SL) interfaces. At high C-S, however, all of the DDAB drops wet in a Wenzel mode. Based on a Gibbsian thermodynamic analysis, we find that for the two types of superhydrophobic surfaces used, the Wenzel state has the lowest thermodynamic energy and thus is more favorable theoretically. The CB state, however, is metastable at low C-S due to a thermodynamic energy barrier. The metastable CB wetting state becomes more stable on the SH microtextures with greater phi and r, in agreement with our experimental observations. Finally, we generalize this surface-energy analysis to provide useful designs of surface parameters for a DDAB-laden surfactant droplet on the SH surface with a stable and robust CB state.