This work aimed to determine the influence of biopolymer coatings based on pumpkin oil cake, with and without the addition of Mentha piperita essential oil, on the quality and shelf-life of the Afus Ali variety of grapes, stored at room temperature and in the refrigerator. Furthermore, a 10% (w/w) aqueous solution of composite pumpkin oil cake (PuOC) with the addition of 30% glycerol was prepared at 60 °C and pH 10. The active biopolymer coating was prepared similarly by adding 1% (v/v) Mentha piperita essential oil. The quality of packed grapes was tested by determining the dry matter content, total sugar content, total acidity, alcohol content, total phenolic compounds content, and total flavonoid content, as well as by determining the antioxidant activity, through the application of the DPPH, FRAP and ABTS tests. Additionally, microbiological parameters were investigated: total aerobic microbial count, yeasts, and molds. The obtained results proved that in all tested samples, over a certain period of time, the content of dry matter, content of phenolic and flavonoids substances and sugar content decreased as a consequence of the spoilage of grapes, that is, the consumption of sugar for the production of alcohol, which consequently leads to the total acidity increasing. The application of lower storage temperatures and active coating (with Mentha piperita essential oil) had a positive effect on all inevitable reactions. Grapes’ antioxidant potential may be enhanced or maintained by applying PuOC coating with or without Mentha piperita essential oil, which is best observed in the case of the DPPH test. The uncoated sample stored at room temperature had the largest decrease in DPPH values during storage, with changes ranging from 2.119 mg/g to 1.471 μmol mg/g. The samples, coated with PuOC and PuOC with the addition of essential oil, had uniform DPPH values throughout the entire storage period. Additionally, regarding phenolic content, at the end of storage period the highest phenolic content was observed in samples with active coating stored at room temperature (734.746 ± 2.462) and at refrigerator temperature (680.827 ± 0.448) compared with untreated samples and with samples with plain PuOC coating. The presence of active essential oil in the applied coating significantly affected the microbiological profile of grapes during the storage period. Besides the positive impact of the applied lower storage temperature, the effectiveness of the applied active packaging is even greater (microbiological results were in the order of PuOC+essential oil < PuOC < Control). The developed artificial neural networks were found to be adequate for modeling the microbiological profile, antioxidant activity, phenolic and flavonoid content.