You can do a few things. The most streamline way is to download modded coats that are only ytd's. The ones that do not come with custom textures, since they're blended with base textures nothing is overwritten and you can mod every individual horse in the geme. Fortunately these are the majority of the modded coats out there. They actually have the majority of the best coats too.
When custom textures are involved that's when things start to get tricky. I'd avoid using them as much as possible unless you're picky or you're hell bent on a certain coat, coats or a certain custom breed. You may have to sacrifice a base game breed or coat and just not look at it unfortunately. I'm pretty sure if you have a modded coat using certain base game textures that are overwritten by custom horses it could break your other custom coats. If you make your own horse coats I don't think it's possible to not override other coats.
When modding with custom textures the best move is trial and error. As much as a pain it is I'd start a test save and download rampage or whatever to spawn all horses in the game to make sure things look okay, go back and forth from the game to editing horse files.. it's a lot of rebooting the game but it's the best way. You never know a custom texture change could make another modded horse look better.. typically doesn't though.