Concentrating acetic acid from vinegar
If I understand correctly, what you described can be seen as a form of fractional freezing.

This is done in order to make alcoholic beverages more alcoholic (Eisbock is an example): the beverage is left to partially freeze and the ice is removed.
Since ethanol has a lower melting point (-114 °C) than water (0 °C), this effectively removes more water than ethanol.

But in your case, since acetic acid has a higher melting point (16 °C) than water, the solids will have a higher concentration of acetic acid and you would want to keep that instead of the liquid.