Due to their markedly distinct protein compositions and structures, goat milk and cow milk display substantially different characteristics. In this study, the quality and composition of goat milk and cow milk were studied after being refrigerated at 4 °C for 7 days, with a particular focus on protein oxidation and aggregation states. The results revealed that alongside increases in acidity, microbial colony count, and hydrolysis, there was a significant change in the protein aggregation state beginning on the second day. This change was characterized by increased turbidity, an elevated centrifugal sedimentation rate, and a right-shifted particle size distribution. After seven days of refrigeration, the centrifugal sedimentation rate of goat milk increased from 0.53% to 0.97%, whereas that of cow milk rose from 0.41% to 0.58%. The degree of aggregation was significantly greater in goat milk compared to cow milk. Additionally, both protein and lipids exhibited substantial oxidation, with the degree of oxidation more pronounced in goat milk than in cow milk. The malondialdehyde (MDA) content increased from 0.047 μg/mL to 0.241 μg/mL in goat milk and from 0.058 μg/mL to 0.178 μg/mL in cow milk. The results suggest that goat milk was more prone to oxidation, which further reduced its stability. Therefore, in the storage and transportation of dairy products before processing, it is essential not only to monitor sanitary conditions but also to effectively control protein oxidation to enhance the quality of milk processing.