Radiative equilibrium studies that place Earth-like exoplanets on different circular orbits from the parent star do not fully sample the range of plausible habitability conditions in planetary systems. In the outer regions of the habitable zone, the risk of transitioning into a globally frozen "snowball" state poses a threat to the habitability. Here, we use a one-dimensional energy balance climate model (EBM) to examine how obliquity, spin rate, orbital eccentricity, and the fraction of the surface covered by ocean might influence the onset of such a snowball state. Since, for constant semimajor axis, the annual mean stellar irradiation scales with (1-e^2)^(-1/2), one might expect the greatest habitable semimajor axis to scale as (1-e^2)^(-1/4). We find that this standard simple ansatz provides a reasonable lower bound on the outer boundary of the habitable zone, but the influence of both obliquity and ocean fraction can be profound in the context of planets on eccentric orbits. For planets with eccentricity 0.5, our EBM suggests that the greatest habitable semimajor axis can vary by more than 0.8 AU (78%!) depending on obliquity, with higher obliquity worlds generally more stable against snowball transitions. One might also expect that the long winter at an eccentric planet's apoastron would render it more susceptible to global freezing. Our models suggest that this is not a significant risk for Earth-like planets around Sun-like stars, as considered here, since such planets are buffered by the thermal inertia provided by oceans covering at least 10% of their surface. Nevertheless, the extreme temperature variations achieved on highly eccentric exo-Earths raise questions about the adaptability of life to marginally or transiently habitable conditions.< Leer menos