Ice cubes melt because they are frozen water; when placed at a temperature above 32 degrees Fahrenheit while at 1 atmosphere of pressure, they undergo a phase transition to liquid water. The melting and freezing points of water are mostly the same, especially when gas is present.
While ice melts above 32 degrees Fahrenheit, if water is free of gas or any nucleating points, it can actually get supercooled without freezing all the way down to minus 43.6 degrees Fahrenheit, placing its melting point much higher than its freezing point. Additionally, ice also melts faster in water than in air because water conducts heat better than air. Inside water, heat reaches the ice 20 times quicker than in air, so it melts more rapidly even when both the water and air have the same temperature.
Salt can also change ice's melting point and prevent melting ice from refreezing. When water is mixed with salt, the freezing point is lowered, and 20 degrees Fahrenheit is needed to freeze a 10-percent salt solution, or 2 degrees Fahrenheit to freeze a 20-percent salt solution. When salt is used to melt road ice and snow, the surface temperature needs to be more than 15 degrees Fahrenheit, or the salt won't have any effect because it cannot get into the solid water to start the melting process.