Grapevine budbreak is a key phenological stage of seasonal development, which serves as a signal for the onset of active growth. This is also when grape plants are most vulnerable to damage from freezing temperatures. Hence, it is important for winegrowers to anticipate the day of budbreak occurrence to protect their vineyards from late spring frost events. This work investigates deep learning for budbreak prediction using data collected for multiple grape cultivars. While some cultivars have over 30 seasons of data others have as little as 4 seasons, which can adversely impact prediction accuracy. To address this issue, we investigate multi-task learning, which combines data across all cultivars to make predictions for individual cultivars. Our main result shows that several variants of multi-task learning are all able to significantly improve prediction accuracy compared to learning for each cultivar independently.