If you want anything more complex than extremeophile bacteria, you’ll need an atmosphere, and that’s something you won’t have if if all freezes on the “night pole”.
Additionally, large bodies of liquid water would be scarce; if a lake extends onto the day side, it’ll boil away until it doesn’t. If it extends onto the night side, it’ll be frozen, though I’m not entirely sure of what the fluid mechanics of the resulting situation would look like; you might get cycles of the ice building up and breaking off into the rest of the lake.
If you want anything more complex than extremeophile bacteria, you’ll need an atmosphere, and that’s something you won’t have if if all freezes on the “night pole”.
Additionally, large bodies of liquid water would be scarce; if a lake extends onto the day side, it’ll boil away until it doesn’t. If it extends onto the night side, it’ll be frozen, though I’m not entirely sure of what the fluid mechanics of the resulting situation would look like; you might get cycles of the ice building up and breaking off into the rest of the lake.