One of the best and simplest ways to help a horse grow out their mane or tail better is to put it up in braids. This prevents the hair from getting pulled out or rubbed off, which causes the mane and tail to get shorter. Get tiny little ruber hair elastics (you can even buy the ones meant for people) and make small, simple braids in the horse's mane. You don't want to make them so tight that it's uncomfortable for the horse, but you don't want them too loose either or they will fall out. It works well to make the braid loose at the begining of the braid, and tighter down towards the end. You can leave this braids in for quite a while and just redo them when the start to get frizzy or come undone. Learn how to properly braid and wrap your horses tail. I'm not as experienced at wraping tails (my horse never needed it) but you can find lots of info online about it. Then when it comes time to show, unbraid everything, wash and condition the hair, and comb the hair carefully to get out any snarls. Comb the mane and tail only as much as necisary. If you keep the hair braided you won't need to comb it as often. Having braids in the mane in tail isn't as pretty as having loose, flowing hair. But you will sure notice the difference when it comes time to show your horse off!
You can also get leave in conditioners to improve the quality of your horses hair.
I hope that was helpful. Your horse is beautiful by the way.