Yes, chewing ice is bad for your teeth and your gums. As this says:
“Chewing on ice can cause gum injury, microscopic fractures in enamel (which can become larger fractures), and even broken teeth. Chewing ice is especially bad for those who have braces or have just had dental work done. And for those with sensitive teeth, chewing ice will most likely worsen, rather than numb, the pain.
There are many reasons that a person might chew on ice. Some people just like having something to chew on. If you’re one of those people, you might want to switch to sugarless gum. If it’s crunch you crave, try carrot sticks, celery, or apples.
The desire to chew ice cubes may also be a symptom of iron-deficiency anemia or other physical or emotional conditions, such as nutritional deficiencies, stress, obsessive-compulsive disorder, or developmental disorders. This is known as pica, which refers to eating or wanting to eat substances that have no nutritional value, including ice, clay, cornstarch, and paper. ”
So just say no.