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, the concentration of water in ice is 100%, but the concentration of water in the mixture is much less. So the 2 way movement of liquid water to frozen water favors frozen water because there are more molecules of water in the ice than out in the solution. 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.