MycroftJr's height slider collab result affects horses. Someone should use my 'mod patch framework' mod and create a patch for the height sliders that adds a UI and functionality for horses, please. The template is already included in the mod as it comes with a UI interaction to adjust sim's height- just not for horses. It looks like the author is also open to submissions of improvements for the mod. :)
To use the height slider as it is right now, download the mod linked above (the height sliders) and you must get the horse's sim ID in game cheat console via sims.get_sim_id_by_name First Last
If they have a last name you MUST include it. If they don't, only use the first name.
After you get the ID, you can use a value between -100 (13 hand pony) and 100 (18 hand giant.) They are both shown in the video. The command to change their height in the cheat console during gameplay unpaused is:
set_height # ID
Working example, with my horse's ID inputted:
set_height 100 135409245365743136