Veterinary medicine is experiencing a digital transformation driven by Artificial Intelligence (AI) applications in diagnostic imaging, disease prediction, clinical decision support, wearable monitoring, and telemedicine. This systematic survey, following the PRISMA 2020 reporting framework, synthesizes research published between 2013 and 2025 to categorize the taxonomy of AI applications, from convolutional neural networks for radiography to large language models (LLMs) for clinical consultation, and to evaluate the current state of AI and deep learning (DL) in veterinary digital health. Using predefined eligibility criteria, 22 studies met the inclusion criteria, comprising 18 primary evidence studies and 4 supporting domain/prototype studies. These studies were classified according to major application domains, including diagnostic imaging, predictive analytics, wearable monitoring, livestock health management, clinical decision support, and emerging LLM-based veterinary systems. The included studies indicate significant advancements in automated radiography, cytology, cardiovascular disease detection, dermatology, oncology, and clinical decision support, highlighting the potential of AI to enhance diagnostic accuracy, early disease detection, and clinical efficiency. Nevertheless, widespread clinical adoption is limited by fragmented datasets, species diversity, insufficient external validation, the opaque nature of many AI algorithms, and the absence of prospective real-world clinical evaluation. While LLM-based veterinary applications exhibit considerable promise, their implementation is still in its early stages, highlighting the necessity for rigorous validation prior to routine clinical use. This survey offers a structured synthesis of current AI applications in veterinary digital health and identifies key methodological limitations, implementation barriers, and future research priorities. Overall, the findings emphasize the importance of standardized datasets, robust model validation, explainable AI (XAI), and interdisciplinary collaboration to ensure the safe, reliable, and ethical integration of AI into veterinary medicine.