The difficulty and prestige of a competition is determined by its tier. A competition always has a tier, and is open for horses of the same tier.
The tiers (lowest first)
5 - Maiden
4 - Novice
3 - Intermediate
2 - Advanced
1 - Grand Prix
When a horse starts competing, it starts in the Maiden tier. If it gets good results in the Maiden tier, it will eventually level up to the Novice tier. Only then can it compete in the Novice tier.
The horse has one tier for its Global Horse/Pony career, and one for its Breeder's Cup. The tier is the horse's permanent level and will never reset.
The jump heights & spreads are determined by the tier. Each tier has its own jump heights. The Breeder's Cup classes are adjusted to suit each specific breed. For example, the heights in the SWB classes are higher than the Friesian classes. That way, each breed can compete on a level suitable for them.
When a new season starts, all courses are locked and need to be unlocked. Unlocking of courses is on a player-level, so each horse does not have to unlock the courses again, and it doesn't matter which horse is used to unlock courses.
To unlock the next course, or the courses of the next tier, a clear round (0 penalties) is required. The tier of the horse doesn't matter, and the amount of ribbons won (if any) doesn't matter.
In order for a horse to compete in a higher tier, it needs to level up. The horse gets tier XP through competing in its current tier, and the better the result, the more XP will it get. A horse that consistently gets bad results with lots of penalties indicates that it's not ready for the next tier, and it will gain very little XP.
In order to maximize a horse's show jumping career, it needs to both train and compete. Whenever a horse is ready to level up to the next tier, it's capability is judged. If it's determined that the horse doesn't have enough capacity, it will not be allowed to level up. When this happens, one of two scenarios occur:
The horse has the potential to level up, but it needs more training in one or more stats
The horse has too low potential to level up
If the horse needs more training, the player can go back to training and then try to level up again. If the potential is too low, the horse has reached its maximum capacity and can not level up. All horses have a limit to their potential, and not all of them can become a Grand Prix horse.
A horse can always compete in lower tiers than its current tier. This is useful for unlocking courses in a new season, or when the player wants to compete in a low-stakes setting, to get practice etc.
Using an overqualified horse does not give the horse any tier XP, and the result is excluded from the leaderboards.