I really enjoyed Aomawa Shields‘s dissertation talk in the “Extrasolar Planets: Host Stars and Interactions” session, in which she discussed how different stellar types could influence the climates of putative Earth-like planets.
She highlighted how the ice-albedo feedback would operate differently on planets orbiting M-dwarfs as compared to those orbiting F-stars. Since they are so cool, M-dwarfs shine primarily in infrared (IR) wavelengths, while F-stars are much hotter and emit in the visible and ultraviolet (UV). At the same time, water ice primarily absorbs IR but reflects visible light.
Therefore, around an M-dwarf, the ice on an Earth-like planet’s surface would absorb a lot of the stellar insolation, heating the planet, while around an F-star, the ice would reflect it, keeping the planet cool. As a consequence, Shields argued that M-dwarf planets have climates more stable against global ice ages than F-star planets. So although there may be other challenges to life on an M-dwarf planet, climate stability is probably not one of them.