Ice cream is scoopable below 0 C. What is sugar really doing there?

Answer: Keeping some syrup liquid

Sweetness hides hardness — Not quite. Sweetness can change how pleasant a frozen dessert feels, but it does not physically make a hard ice block scoopable. Sugar's deeper job is in the water phase: dissolved molecules change the freezing point. That is why texture changes when you swap sucrose, dextrose, or glucose, even before flavor preference enters.

Keeping some syrup liquid ✓ — Right. Dissolved sugar lowers the freezing point, so not all the water freezes solid at normal ice-cream temperatures. Guelph's ice-cream text gives a useful scale: around -16 C, only about 72% of the water is frozen in typical ice cream. The rest is a concentrated syrup that carries flavor and softness. Too little sugar makes a hard block; too much can make it slushy.

Helping fat trap air — Not quite. Fat and emulsifiers help build the foam-and-fat structure, so trapped air does matter to texture. But sugar's main role here is colligative: dissolved molecules change how water freezes. The same principle is why salt melts ice on roads, though the taste and food structure are obviously different.