This paper introduces a novel approach to budgeted online active learning from finite-horizon data streams with extremely limited labeling budgets. In agricultural applications, such streams might include daily weather data over a growing season, and labels require costly measurements of weather-dependent plant characteristics. Our method integrates two key sources of prior information: a collection of preexisting expert predictors and episodic behavioral knowledge of the experts based on unlabeled data streams. Unlike previous research on online active learning with experts, our work simultaneously considers query budgets, finite horizons, and episodic knowledge, enabling effective learning in applications with severely limited labeling capacity. We demonstrate the utility of our approach through experiments on various prediction problems derived from both a realistic agricultural crop simulator and real-world data from multiple grape cultivars. The results show that our method significantly outperforms baseline expert predictions, uniform query selection, and existing approaches that consider budgets and limited horizons but neglect episodic knowledge, even under highly constrained labeling budgets.