I built a snowman farm in minecraft with a few friends and no snowman drops snow?
They don't "drop" snow, but place a layer of snow under them, which you have to break down with the shovel.
Snow Golems do not spawn snow under them in some biomes,
there are also biomes in which snow golems only spawn from a certain height of snow. (Since it is colder further up)
They also don't leave snow on hoppers.
There's an article in the English Minecraft Wiki: https://minecraft.gamepedia.com/...ow_farming
Snow Golems do not spawn snow under them in some biomes,
They die in this biome anyway, don't they?
You formulate it as if there were biomes in which they do not generate snow, but also do not die. Which one?
As I just reread after you die in these biomes as you write it.
So only the altitude information remains to be taken into account.
According to MC Wiki:
Above Y≈64 in plains, sunflower plains, swamps (including swamp hills), and beaches
Above Y≈124 in mushroom fields and shore
Above Y≈154 in jungles and variants
Above Y≈184 in savanna plateau and shattered savanna plateau
Above Y≈244 in shattered savanna