What does it mean when my horses’ stat bars turn light pink. And how..

A horse's stats will turn light pink when they've reached the maximum level they can be trained to in that discipline. A horse can be trained to one level less than the amount of horseshoes they have in that discipline (don't ask me why). So, a horse with 4 horseshoes in agility can be trained to level 3 using dressage, just like a horse with 3 horseshoes in muscle strength can be trained to level 2 using showjumping, etc, etc.

Unfortunately, if you have finished training your horse in the paddock and it still only has 2-3 horseshoes, you cannot stop the issue of their stats turning light pink, no matter how much you train them in that discipline, they will not be able to advance further. The only solution is to buy a horse that has more horseshoes, or bread a foal, which will generally have the same, if not more, horseshoes than it's parents (as well as more time for paddock training, since they're young).

Ideally, you want to buy, or breed, a horse with 4 horseshoes in every discipline, so they can be trained to a minimum of level 3 so you can win any competitions in that discipline. It is not actually necessary to train to level 4, you can still win all competitions at level 3 in every discipline.

A horse's horseshoes can be increased by a maximum of 1 for each discipline, that is, if you take the time to train them in the paddock. This is quite a long process, but it is the only way to increase horseshoes in a horse (or foal) you already own. This way, a horse that has 4 horseshoes in every discipline can gain 5 horseshoes in all disciplines and ultimately be trained to the maximum of level 4 in all disciplines. (I hope this isn't too confusing - I didn't create the game!)

I normally breed foals with 4 horseshoes all round, and train them while they are young (and can't do anything else), so that by the time they are adults and can compete, they have 5 horseshoes and I can train them up in every discipline. (You also level up in dressage, cross country and showjumping a lot faster if you train your horses/foals in the paddock first!)

I really hope this helps, since I also ran into this issue when I was starting out in the game, because it doesn't explain it very well. Actually, this game doesn't explain a lot of things very well, but anyway...

Good luck!