If I remember correctly, making a compound of a liquid and salt will lower the freezing temperature of the compound. (It would need to get colder to become solid, which would take more time) I don't know if ice cream turns out better if it's frozen for a longer time, though.
So, two changes I can see are that the ice cream would take longer to freeze if it had salt in the mixture, and that the ice cream with the salt would melt more slowly (maybe someone could check me on this) when kept at room temperature.
Edit: Or would the ice cream with the salt melt more quickly because it freezes at a lower temperature?