well from what i read, the oil is a big attractor for dirt, but if you don't use a bunch (i used a medium amount), then it should be fine. It was a little dusty around the outside of the braid, but I rinsed it after 2 days of soaking, then rebraided it and after i took it out, this is how it looked.
I have long hair (down to my tail bone) and I use coconut oil all the time on my own hair. It's great if you have long hair and don't want the ends to dry out etc. It's great also as a pre-wash deep conditioner, i.e oil it up really well the night before, braid it up and sleep on it and then wash in the morning.
Anyway the tail on your horse look great, and if you're curious you can use the coconut oil in your own hair too
ETA: Coconut oil is one of the few easily available oils that really mimic the natural oils found in human hair so it soaks right into the hair rather than just coating it. It clearly isn't too different from the natural horse oils either.