Let's talk more about freezing point depression.
Notice that ice cream melts differently than ice. Ice stays hard until it melts. Ice cream gradually get softer and softer.
Ice is a pure substance but ice cream is a mixture. In other words, there are other chemicals that get in the way of ice freezing. So you have get colder than 0°C to get it to freeze.
About 30% of the water in ice cream never freezes because of the high level of dissolved solids like sugar, fats, and proteins.