The presence or absence of gravity is a red herring in this scenario. Completely irrelevant. The water would not fall off the disk because of gravity, unless there were some very distant gravitational source pulling it away from the planet, nor would it stay on the disk because of gravity. If gravity DID exist, the water would form into a ball at the center, not flat on the disk surface.
There is another much more important factor.
Centripetal/centrifugal force. If the disk-earth were spinning', the water would be flung off simply because it was given a velocity, and inertia would keep it going in one direction (a tangent to the disk). Thus, the walls would be required to counter this centripetal/centrifugal force. However, what WOULD happen is that the water would bunch up against this wall, and it would then flow over it, unless the ice wall itself had a lip on it. Spin a flat disk around your head with water on it. The water will certainly not remain there. But put the water in a pail? The sides of the pail keep it in.
So, don't spin the planetary disk at all. No centripetal/centrifugal force. No gravity, so the water does not all bunch up into a ball. Nothing pulling the water 'down', so it does not flow off.
OOOps, forgot about surface tension.
Surface tension would tend, just like a drop of water, to keep the water 'bunched up' so it does not slide off. Ever see the pictures from the ISS crew, drinking water, spilling it on a 'desk'? Same idea.
So your ice walls have a very reduced task. Surface tension would keep the water flat against the disk.
The cold of space would keep the walls ice, as log as they were protected from radiation, and sublimation.
So, coat the ice with a thick layer of lipids that form cell membranes. Make one end hydrophobic, one end hydrophilic. They would stay only on the surface of the ice, with the hydrophobic end facing outside and the hydrophilic end bound to the ice. In effect, you are exponentially increasing the surface tension. Since lipids can be very long polymers, the intertwined polymer lipids would form a very strong 'skin' around the ice. This would prevent sublimation.
Since water, and ice, are very good shields against radiation (it has been posited to put huge water tanks around the Martian transport craft to protect the inhabitants), and allow the hydrophobic end of the lipids to form a very reflective coating, and your problem is solved.
No centripetal/centrifugal force to 'spin' the water away, no gravity to cause it to flow 'down' (wherever 'down' is), or to the center, an ice wall protected from sublimation and radiation, kept in place by very long chain polymers, and surface tension keeping it from floating off into space.
Except, well, there is the problem of preventing ALL the water from freezing. But then, if it all froze, problem solved. It would be one huge iceberg covering the planet.
If you DID allow gravity, your situation is greatly simplified. Spin the disk at such a speed that the gravitational pull causing the water to 'ball up' is perfectly balanced by the centripetal/centrifugal force of the spinning water. As long as the forces balanced, the water would stay on forever (assuming sublimation is taken care of).