there are mods on Nexus that allows you to replace storymode horses with online horses. Go here https://www.nexusmods.com/reddeadredemption2/mods/598 and https://www.nexusmods.com/reddeadredemption2/mods/714 and https://www.nexusmods.com/reddeadredemption2/mods/889 also this one has the chestnut turkoman coat https://www.nexusmods.com/reddeadredemption2/mods/815
i hope this helps you, currently you cant add them in you can only replace the coats on existing horses in the game. you need lennys mod loader to use this mod. it will have instructions on how to install and use it. Best of luck!
Go to nexusmods.com there's this person that is making retextured/reskinned horses and has already made alternate coats for MFT, Morgans, Turkomans, Nakotas, Mustangs, and Arabians. Look up bolju, that's their name.