You need to replace the default sounds with silence, then write a custom mission trigger that plays the "correct" sound for each horse agent based on what item the horse actually is.
You can also add the flag
to the non-horses, so that you need the custom sound only for those ones.
At TLD they have different sounds,
is the mission template you need to look for here: https://github.com/tldmod/tldmod/blob/master/ModuleSystem/module_mission_templates_TLD.py
Not sure about the place at module_sounds.py at which you need to look at but now you have already a good start to find the rest.
You can't have a new set of animations for them. All mounts are using the same animations.