That depends on whether the ice is sea ice (floating on the ocean), or land ice (sitting on land). If it's land ice, then it doesn't interact much directly, although if the land ice melts then the resulting liquid water flows into the ocean and raises the sea level because there's now more water in the ocean.

The sea ice acts like any floating object , except that it, too, can melt.

Archimedes' Law states that a floating object displaces its weight , which means that a melting iceberg will not raise sea level because the amount of water that it will add to the ocean exactly equals the amount of water that it displaces by floating.

Ice floats on water, so the water will run down off the ice if it can find a path downhill. But there will also be pools of water on the ice, if the water just warms the ice under it without any way to flow downhill. And ice caps will also have earth - dirt and rocks - under a parts of them.