This is correct, and it isn't just associated with acids. It's because of an effect called 'freezing point depression', which is the same reason salt lowers the freezing point of water while raising its boiling point.

There are a few explanations as to why this happens, with the easiest being this: if you add something that can't freeze to something that can, then the whole thing will need to lose more energy to allow the whole mass to solidify because the un-freezing stuff physically interferes with the attempts of the freezing stuff to bind together.

However, there is also the additional aspect of vapor pressure, which comes into play when adding things that can freeze to another thing that also freezes, but at a different temperature. I don't really understand that at all, so I will pull from the Wikipedia article on it:

The freezing point is the temperature at which the liquid solvent and solid solvent are at equilibrium, so that their vapor pressures are equal. When a non-volatile solute is added to a volatile liquid solvent, the solution vapour pressure will be lower than that of the pure solvent. As a result, the solid will reach equilibrium with the solution at a lower temperature than with the pure solvent. This explanation in terms of vapor pressure is equivalent to the argument based on chemical potential, since the chemical potential of a vapor is logarithmically related to pressure. All of the colligative properties result from a lowering of the chemical potential of the solvent in the presence of a solute. This lowering is an entropy effect. The greater randomness of the solution (as compared to the pure solvent) acts in opposition to freezing, so that a lower temperature must be reached, over a broader range, before equilibrium between the liquid solution and solid solution phases is achieved. Melting point determinations are commonly exploited in organic chemistry to aid in identifying substances and to ascertain their purity.

So, TL;DR is that chemistry is weird, things react weird at the molecular level because of energy states, and that is what allows us to make ice cream!