Sugar controls the amount of ice that forms during product freezing. This ensures that the ice cream is soft enough to be scooped up and eaten. It also gives thickness to the product and makes it stable to thermal shocks (entering and leaving the freezer). Usually different sugars, honey or syrups.
It adds sweetness but also improves texture and body. It also lowers the freezing point of the mix, ensuring that the ice cream doesn't freeze like a rock. In other words, reducing the consumption of sweeteners (for dietary or health reasons, for example) not only affects sweetness, but could also jeopardize the “structure” and stability of ice cream.