We continue to investigate the binary system Kepler-16, consisting of a K-type main-sequence star, a red dwarf and a circumbinary Saturnian planet. As part of our study, we describe the system's habitable zone based on different climate models. We also report on stability investigations for possible Earth-mass Trojans while expanding a previous study by B. L. Quarles and collaborators given in 2012. For the climate models, we carefully consider the relevance of the system's parameters. Furthermore, we pursue new stability simulations for the Earth-mass objects starting along the orbit of Kepler-16b. The eccentricity distribution as obtained prefers values close to circular, whereas the inclination distribution remains flat. The stable solutions are distributed near the co-orbital Lagrangian points, thus enhancing the plausibility that Earth-mass Trojans might be able to exist in the Kepler-16(AB) system.