Frozen food is exposed to inevitable temperature changes during its storage, transport, and at the point of sale, which implies a significant impact on its properties and quality. Thus, the study of the effect of the formation of crystals on both the surface of the meat and the container when it is kept frozen, involving the thermodynamic analysis and changes that occurred at the structural level, is necessary. In this research, pork meat from Longissimus thoracis muscle was used, which was cut into plates and packed with two types of food-grade films: (1) Polyvinyl Chloride (PVC) and (2) low-density polyethylene (LDPE). Samples were frozen by indirect contact with nitrogen up to −40 ± 0.5 °C and subsequently stored at −20 ± 1 °C in a chamber from 0 to 15 days. The frost thickness was evaluated by the image superposition method. FTIR spectra were obtained by means of an Attenuated Total Reflectance (ATR) accessory, and thermal changes were determined by Modulated Differential Scanning Calorimetry (MDSC). It was found that the thickness of the frost on the surface of the meat is less when it is packaged with PVC due to the characteristics of the polymer matrix of the package. Furthermore, there were important changes at the molecular level identified by FTIR and MDSC, indicating significant differences (p < 0.05) between the samples. In general, PVC films were more stable at lower temperatures, allowing a small number of changes in the meat surface due to temperature fluctuations.