It's all in the brew. Cold-brewing coffee grounds produces a smooth and less acidic cup of joe, not to mention cuts out the pouring hot liquid over ice step. This is usually done with a french press, but can also be done in a simpler method, without specialized equipment.
If you are an iced coffee drinker, the difference between cold-brewing it and just letting hot coffee cool off is remarkable.
What you need to do is fill a glass jar, (a clean recycled spaghetti sauce jar works great) with a mixture of cold water and med-course ground coffee. I use one rounded coffee scoop to a whole jar of water. Stir this mixture up and let it set overnight.
In the morning, strain through a filter or cheesecloth. This yields a more caffeinated brew and apparently is easier to guzzle down because of the lower acidity. Try diluting it with some water or milk, or beware of the caffeine jitter fest. I fill my cup about half full of the coffee, add a tsp of sugar and top it off the rest of the way with milk.
For my ice cubes, I fill a couple ice cube trays with this mixture, freeze, and then store them in a ziploc bag in the freezer. That keeps my melting ice from diluting my drink.