The amount of times per year you run your horses depends on your aim, I think. Are you attempting to breed/select decent online league horses, or are you playing purely for single-player fun.
When playing just for fun I tend to race my horses as many times per year as they can handle (they only run when they are at peak fitness, not when they're tired). I also keep records of how much a horse made during its entire career, trying to beat my top records all the time, which means running them as much as I can while still winning.
For league (not that I stuck with the league for long, lol, nor am I any expert - far from it) I tended to run my horses very sparingly, generally only a couple of times before exporting mid-year, for a total of four races per year, per horse. This was mainly to allow me to get through seasons more quickly, as well as to prevent over-racing, thus diminishing potential growth (not entirely sure that the game works this way, just a feeling).
As for when to retire to stud, I always retire when they turn five, not racing them at all before retiring that season (this is to keep my sheet of earnings fair - all horses get the same amount of time to make their money). I don't think it matters when you retire to stud in terms of offspring's talent/potential. I've also found that most horses tend to go downhill after their fourth year and I would rather get as many foals out of the good ones as possible, rather than keep running them when they have passed their peak. I play only flat, though, for jumps obviously the ages are different in regards to peak form, etc.
I don't tend to plan out a season for my horses, prefer running them when they are fit, in the most appropriate race for their ability/preferences.
If you have a world beater, it is the same as any other horse in terms of how much racing it can take- keep an eye on it's fitness and on the head lad's comments in the training section. I've heard that over racing during two year old season can hinder development later on, not sure about three/four. So, according to what I've heard, you could mess up a world beater by overracing during their two year old year, however after that I'm not sure.
It is an awesome game, hey? 
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