yes all horses jumps bars increase with age. At 2 they have almost nothing in most cases and by 10 in some cases they are really high. The only way to tell if a horse will be a good jumper or not is to go into the adjust training screen and look at the horse information. The one's that say that the jumping are good will normally be good in NH. If no jumping bar appears as in the case of my horse Sellout then they are normally good hurdlers but if they have a jumps bar like balloon king bar then they are better chasers.
Although his bar is really high
You will also notice that his potential bar has decreased. At 2 I have yet to see a jumps horse with a full potential bar including the light green bit. But by 5 I have seen a few. There is no indication besides maybe breeding as to which horses potential bars will increase.
I would be pretty ecstatic with a horse with those stats.. I don't have really high jumps bars and keep breeding with game horses to try find one. I have managed to get really high fast jumping bars but not the normal jumps bar or safe jumping bar
