Cold temperatures during fall and spring have the potential to cause frost damage to grapevines and other fruit plants, which can significantly decrease harvest yields. To help prevent these losses, farmers deploy expensive frost mitigation measures, such as, sprinklers, heaters, and wind machines, when they judge that damage may occur. This judgment, however, is challenging because the cold hardiness of plants changes throughout the dormancy period and it is difficult to directly measure. This has led scientists to develop cold hardiness prediction models that can be tuned to different grape cultivars based on laborious field measurement data. In this paper, we study whether deep-learning models can improve cold hardiness prediction for grapes based on data that has been collected over a 30-year time period. A key challenge is that the amount of data per cultivar is highly variable, with some cultivars having only a small amount. For this purpose, we investigate the use of multi-task learning to leverage data across cultivars in order to improve prediction performance for individual cultivars. We evaluate a number of multi-task learning approaches and show that the highest performing approach is able to significantly improve over learning for single cultivars and outperforms the current state-of-the-art scientific model for most cultivars.