Piccolina - what you are looking for is something called grow lights
- which supply artificial sunlight. Not only is there a matter of the UV spectrum they produce but there is also the matter of the intensity of light produced. This Indoor Plant Grow Light Guide
covers the basics - but you probably want to check out several of the sites listed in the first (Google) link.
I honestly do not see where ice cubes would be any more effective or efficient than a much simpler "microdrip" watering system. You can actually make one of those out of an old enema bag, some plastic tubing and connectors from an aquarium shop, and a safety-pin.
How do you feel about growing your own mushrooms, instead?