If there is a bit of ice left in a glass after I have finished a drink then I'll suck on one of the cubes, but I don't purposefully fill glasses with ice to eat.
Eating ice makes the teeth brittle from the cold and chewing it can easily chip and crack a tooth. It is also an abrasive and wears out tooth enamel.
There seems to be a relationship between ice eating and iron defiencies. If you aren't already taking an iron supplement everyday, you should be. Low iron causes extreme fatigue, pale skin, weakness, shortness of breath, headache, lightheadedness, and often cold hands and feet.