The key is in the terminology- the freeze point suppressant must be a solute. Oil won't suppress the freeze point of water because it doesn't dissolve. A small amount of sodium chloride or ethanol will suppress the freeze point of water to -5°C.
The first exception is when the solute stops dissolving. This is called the eutectic point. For example, you can only dissolve 23.3% NaCl in water (by mass). That mixture will freeze at -21.1°C. After that, adding more salt won't reduce the freeze point further.
The second exception is with large amounts. If you mix water and ethanol in a 50/50 mol ratio, which is the solvent and which the solute anymore? You can calculate the freezing point suppression of each with respect to the other and they won't match. Liquid/liquid mixtures also have eutectic points at the minimum freezing point, which is less than the freezing point of either component.
To get the actual freezing point for non-dilute systems, try searching for "solid liquid equilibria", "eutectic point", or "binary phase diagram".