The recently developed Equine Facial Action Coding System (EquiFACS) provides a precise and exhaustive, but laborious, manual labelling method of facial action units of the horse. To automate parts of this process, we propose a Deep Learning-based method to detect EquiFACS units automatically from images. We use a cascade framework; we firstly train several object detectors to detect the predefined Region-of-Interest (ROI), and secondly apply binary classifiers for each action unit in related regions. We experiment with both regular CNNs and a more tailored model transferred from human facial action unit recognition. Promising initial results are presented for nine action units in the eye and lower face regions. Code for the project is publicly available.