The demiplane spell creates a door that leads to another plane of existence:
You create a shadowy door on a flat solid surface that you can see within range. The door is large enough to allow Medium creatures to pass through unhindered. When opened, the door leads to a demiplane that appears to be an empty room 30 feet in each dimension, made of wood or stone. [...]
It seems that this room is the entirety of this plane. There is nothing beyond the ceiling, floor, or walls. In a sense, the ceiling is the limit of the "sky," although if it has weather is questionable.
Given all this, is the space inside a demiplane considered "outdoors" for the purposes of the control weather spell? Control weather requires that:
[...] You must be outdoors to cast this spell. Moving to a place where you don't have a clear path to the sky ends the spell early.