The University of Minnesota Grape Breeding Program has developed cold-hardy wine grape cultivars that have facilitated the establishment of an economically important grape industry for the Midwest region. In recent years, the program has renewed efforts to breed cold-hardy table grapes. Table grapes might require postharvest storage if they are to be transported or stored for any period of time. Rachis dehydration, berry splitting, and decay can affect the postharvest quality of table grapes. In this study, we evaluated these postharvest traits in six released cultivars and nine advanced selections in the breeding program. For two growing seasons, we used industry standard packaging to assess postharvest traits (rachis dehydration, berry splitting, decay, and overall acceptability) at 2, 4, and 6 weeks of cold storage at 2.2 °C. The growing season had a significant effect on postharvest traits; therefore, the two were examined separately. There were significant differences in postharvest storage times for all traits, except berry splitting in 2020. Mean rachis dehydration reached unacceptable values (>3) after 4 weeks of postharvest storage in 2019 and after 6 weeks in 2020. All other trait means remained acceptable for many cultivars even after 6 weeks of postharvest storage. Advanced selections performed at and above the level of released cultivars, suggesting that selections will perform well in cold-hardy regions. The data collected regarding fruit quality and postharvest storage for two seasons will help to inform and improve breeding of cold-hardy grape cultivars.