So these are just ideas, I have no idea if they are even remotely possible and things can always be adjusted and I was thinking what if some horses could have multiple traits?
1.) Aggressive/Wild - Has a chance of doing 1 or 2 heart damage to you if your near it every 20 to 30 minutes?
2.) Protective - Rears at hostiles near you within 4- 6 blocks, does 1-2 heart damage to hostiles.
3.) Cowardly - Gets spooked (Rears and Runs) if hostiles and other possible mobs are around.
4.) Born Leader - They get +20 points along with horses in a 10-15 block area of them?
5.) Rodeo Ready/Bucking Bronco - -15 or -20 xp gain most likely to buck and run with you on it and off of it.
(I may add more later on but if yall have any ideas to add comment down bellow.)
(Idea for rider levels to make them more useful is make it so the more levels you have the harder it is for a horse to buck you off)
(The horses will still rear, you are just less likely to fall off the horse at times but if you want the horse to stop bucking all together you need 100% ground work.)