DMG rules strongly suggest a DM's ruling that does not allow the passage via the Ethereal Plane.
As divibisan's answer states, the DMG rules about movement in the Bordered Ethereal strongly implies that going in and out a Tiny Hut via the Ethereal plane is not possible.
Anyway, this is one possible interpretation of the rules, since the spell description does not say anything about blocking the passage in the Ethereal plane, while there is at least one spell, Wall of Force, that specifies this (emphasis mine):
Nothing can physically pass through the wall. It is immune to all damage and can't be dispelled by dispel magic. A disintegrate spell destroys the wall instantly, however. The wall also extends into the Ethereal Plane, blocking ethereal travel through the wall.