I have a 12 year old doing 145 level jumping in Europe and competes on a weekly basis and I have him on joint supplement. He’s been on it since he was 10. I recommend it if your horse is 10+! That’s the only real thing he’s been getting extra, minus electrolytes, garlic powder etc. Or when he’s not doing so well, some things for digestion etc. He’s not on a lot because he doesn’t need a lot. He is a strong horse so I try not to give him anything extra unless he needs it.
I use polos on his front legs when flatting, and he is ridden 6 days a week with usually one heavy jump day and one light jump day, a hack day, a hill day for his back etc. He also gets out twice a day, so maybe walker in the morning, ride in the afternoon, or ride in the morning, field, or walker, field. A combination based of what he need.
After jumping I run his legs under some cold water and go for a hand walk after but I don’t feel the need to ice unless it’s after a show.
I think suplements are good because is a help for it and a training regine obviously. A rutine but some days you can take it for a walk. You should have its head clean; I don't know if you understand me🙃