How wet should I keep the soil during dormancy?

If you used the tray method for watering your Venus fly trap during the active growing season, then you should remove the Venus Fly Trap from the tray for dormancy. The plant can just be top watered and only enough to moisten the media. Any extra water should be allowed to just run out the bottom. The plant shouldn’t be allowed to stand in water. This will help prevent fungus and root rot from starting.  Over watering, especially during the winter, is the leading cause of death for Venus fly traps in cultivation.