If the Moonbeam spell required the actual moon to be shining down, and somehow focused its light (or similar), you would assume that its text would reflect that. No mention is made of this, nor of the restrictions that it would naturally apply to use of the spell.
This wouldn't just be a problem indoors - consider phases of the moon, daytime, cloudy nights, or even eclipses. In fact, it would be an extremely limited usage spell.
Contrast the Call Lightning spell (Thanks Tashio for providing the text):
PHB Pg.220 Call Lightning
A storm cloud appears in the shape of a cylinder that is 10 feet tall with a 60-foot radius, centered on a point you can see 100 feet directly above you. The spell fails if you can't see a point in the air where the storm cloud could appear (for example, if you are in a room that can't accommodate the cloud).
If you are outdoors in stormy condition when you cast this spell, the spell gives you control over the existing storm instead of creating a new one.
This specifically says that it creates a cloud, includes limitations requiring you to be outdoors or have an incredibly high ceiling, and includes an additional effect if there is a pre-existing storm. Based on this, it seems clear that Moonbeam has no particular source or restriction whatsoever.
Obviously, you are the DM, and you are free to add fluff or requirements as you choose. But I would urge you to consider how limited this spell would become before you do.
Best Answer
If a spell has an effect when it drops someone to 0 HP, it is explicitly mentioned in its description, like disintegrate:
Cone of cold does not outright kill a target reduced to 0 HP. The additional effect only happens if the damage outright kills a creature. In the case of a PC this means either taking massive damage that instantly kills them or auto-failing their last death saving throw because of taking damage (PHB 197).
"Until it thaws" just indicates that this is not magical ice that will remain regardless of the circumstances and will melt as natural ice does. You just need to apply heat, e.g. by leaving it in the sun or judicious application of prestidigitation. They become a "frozen statue", not an "ice sculpture", thus after melting out you get a wet corpse that can be raised normally. I personally would also rule that if you use a high level spell that would restore missing organs, like true resurrection, you can use it directly on the frozen corpse.