Consider a small body at the focal point of a parabolic reflector, and that reflector pointed at empty sky at night.

You effectively have the body radiatively thermally connected to space, and space is cold. So heat radiated from the object goes out to space, and nothing comes back, and thus the object gets colder.

If doesn't work if there are clouds, because clouds are quite warm.

Not much is going on in terms of the 2nd law, because this device is not a closed system (heat is coming in and then later going out) so the 2nd law doesn't apply.