Your horse has a better tail than mine! But I braid my horses tail haha it makes his big QH but look pretty good!
I used to be a pro groom (show jumpers) and I used to pull the horses tail to get rid of all that outwards pointing fuzz!
What discipline are you showing? Because I know you can strategically pull a western horses tail to settle all that fuzz down, without it looking tooooo English
Put some rubber gloves on and pull those side hairs out....it will tame it down, just do it enough to make it look natural