I did not say at any point that your model should extend model entity.
This requires three classes. Your entity class should extend HorseEntity giving you access to all of the GUI, saddling and taming. Your render class should be adjusted to not be using the superfluous classy created, as I previously mentioned. Your model class needs to extend HorseModel – this is how you will inherit the animations and bulk of the model.
Note that AbstractHorseEntity does not have all of the code for horses, only the shared code between the various horse entities.