In order to investigate the mechanism of freezing point depression (FPD) phenomena for polymer solutions and/or swollen rubber vulcanizates, some experiments related to this phenomenon have been carried out at a constant rate of cooling and at low temperatures. Thus far this phenomenon has not been explainable in terms of an ordinary colligative effect. In this study a new mechanism is proposed. In this mechanism, microsyneresis occurs first, because of the lowering of solvent quality with decreasing temperature, followed by crystallization of the (swelling) solvent. The measured freezing point is considered to be mainly dependent on the polymer concentration of the concentrated polymer phase formed by microsyneresis. The concept of local volume fraction is introduced in order to evaluate the polymer concentration of the concentrated polymer phase, and then Flory-Huggins' lattice model theory is extended so as to reproduce the experimental results. The physical meaning of the E-parameter used in the extension of the theory is discussed in detail. The E-parameter is associated with the changes of the excluded volume effect with decreasing temperature and might reflect the degree of formation of microsyneresis.