Good, then these type cuts are minor. Cuts of this type if not gaping or shifting when the tongue is moved do not require stitches. If any movement of the tongue or shifting is present then see the ER doctor. Stitches may be required then.
Keep the area that is cut pressed up against the cheek. Rinse mouth with mild amount of hydrogen peroxide if dirt is present in the cut itself. Continue with the ice water or better yet use small ice cubes on the tongue as can be tolerated.
Use a soft diet for about two days. Avoid any spicy foods for this type cut. Continue to check for healing and bleeding. Any redness or pus coming from the area may require the care of a doctor.
Expect up to about 7 days for healing and possible bad breath. Continue to brush teeth and use mild mouth wash to clean the mouth and tongue area. Sounds as though he will be fine. reply if needed.