Biggest recommendation I have is test your hay or horse's blood and fill in nutrition blanks. To be honest, trying supplements can be a bit of a shot in the dark, when results can take up to 9 months or more to show up. No individual supplement is going to work miracles without the basis of a balanced diet and not all grains/ ration balancers are complimentary to all areas, despite advertisement. For example, I literally could not find one grain or ration balancer in my area that would balance out the high iron, low vitamin E etc in my area. Good growth will be a result of adequate nutrition.
I have heard of biotin helping a little bit. Biotin is a b-vitamin (B7) that helps metabolize food and is both produced in the body and found in food, meaning that is is rarer for a horse to be deficient in biotin. That being said, some research has suggested that increased biotin may help with growth rate and hair/hoof strength. However, research on the relationship between biotin supplementation and growth rate are mixed, most likely because of differences in nutrition, climate, age, etc between horses used in the studies. There is also the fact that there is a lack of consistent regulation in equine supplements, which does not guarantee good quality biotin, nor a certain amount, as indicated on the label.
In short, supplementing with biotin wouldn't hurt, but I'd suggest testing your horse's nutrition first for optimal results.
For other things to do, I recommend finding a nice oil moisturizer on the mane, such as joboba oil etc. I've also used coconut oil in the past, but it does get waxy in cooler weather, so I didn't like it as much. Avoid daily detanglers with silicone in the ingredient lists as they coat the hair strands, which blocks moisture from penetrating the hair and can lead to breakage. However, they may work in your favor if you have access to a wash stall and need to keep mud from drying out the tail.
Brushing hair can lead to breakage, but so can a horse that becomes itchy at the crest, so I think this is dependent on the horse. My horse, who has a very thick mane, can not stand no brushing and will literally itch until he self-roaches his mane. I compromise by using a wide tooth comb and detangler to minimize breakage. I've also tried braid and banding in the past, but have had the best results leaving it loose.