In science there's a concept called "equilibrium" and nature is always trying to reach it. That is when all things are the same, e.g., equal. A cold glass of water in a warm room will grow warmer trying to reach temperature equilibrium with the room it's in (the room will grow slightly cooler during the same process but probably not in any amount measurable except by very precise instruments and that assumes no heat is added to the room). This is why your house always tries to get colder in winter and hotter in summer as it tries to reach equilibrium with the outside.
If your glass of ice water is an adiabatic system (that is, no heat or matter goes in or out) then it will try to reach equilibrium. The water will cool until it is on the verge of freezing and the ice will warm until it is on the verge of melting. They both will be at 32 degrees F (0 C). Again, in an adiabatic system, they will stay like this for pretty much ever. In the real world, of course, there is no such thing as an adiabatic system and heat will seep through the glass into the water warming it a bit, the ice will then melt a bit, soaking up that heat in the process of turning ice into water, and again the ice/water mixture will be at 32 degrees. But eventually all the ice will melt and the water warm.
To freeze ice you have to first cool it to 32 degrees (take out heat) and then you have to leap this barrier called "the latent heat of fusion" but taking out even more heat to turn it into ice. When ice melts, it absorbs the same amount of heat from its surroundings, cooling them. This absorption of heat is how iceboxes worked for years before the invention of refrigeration.
This tendency toward equilibrium is why ice water is so refreshing: the water is just on the verge of freezing. It's as cold as water can get without freezing.
And what does this have to do with life? The water molecule is unique. We all know it's H2O (I can't subscript so I made the "2" small). Here's diagram of a water molecule (somewhat simplified):
The "dipole moment" is a fancy term for saying the water molecule is positively charged on one side, and negatively charged on the other (this has to do with where electrons end up around this molecule due to the properties of the oxygen and hydrogen atoms). Also, the angle between the hydrogen atoms is unique. In an organic molecule like methane (CH4) they would be 90 degrees apart (in three dimensions). These two properties of the water molecule mean that when water freezes, the molecules line up farther apart then when they are liquid. The crystal form of water (i.e, ice) is less dense than the liquid form. We've all experienced this as ice has broken bottles of water left outside overnight and frozen (or forgotten in the freezer where they were put to cool quickly). I think there are a few other molecules where this is true, but none as important as water.
(This property also means that unlike most molecules, it melts under pressure, which is why you can ice skate, ski, and slip on icy sidewalks because as you put pressure on ice, a thin layer of water develops which slides very easily over ice. You may have noticed if you live in northern climates that ice is less slipper the colder it gets, because it doesn't melt as readily.)
Because ice is less dense than water, it floats. "Big deal," you say. "Everyone knows that," you say. Well, yes, we are so accustom to it we don't think about it. But think about this. If ice didn't float it would form on the surface (coldest part) of a lake, river, stream, ocean, etc. and then sink. Then more ice would form and sink. And that would continue until the entire body of water was ice. In the summer, a bit of the surface would melt, but most of the volume would remain ice. And under those conditions there would not be liquid water available year-round to support life. Have an ice age or two and the tropics would all be icy, too.
So, while you are enjoying that refreshing glass of ice water, remember it's the water molecule that makes that water so refreshing and makes it possible for there to be life on our planet.