There's actually some argument about this. Depending on who you ask, you'll get answers varying from 18 months to 6 years old - and you'll hear good arguments on either side.
I grew up with an answer of "Three and a half - with full work not starting until 4." Most racehorses, however, are broken to ride at about 18 months - long before they stop growing. And in the United States, riding horses are usually broken somewhere between 18 months and 2 so they can be shown in under saddle futurities.
It's easier to train a younger horse, but training them too young can cause joint and back damage. Breaking horses in younger than three is a relatively recent thing that came out of the popularity of 2 year old races (the Kentucky Derby used to be considered a "futurity" for young prospects, not the peak of a horse's career). So, for wordbuilding purposes, it's probably best to assume that most people are breaking horses at 3-4. In modern horse training circles we talk about whether the joints have "closed" and many feel it is cruel to ride a horse before certain joints have closed, that is, stopped growing and developing. I still hold to the "four years for full work" rule.
Harness horses can be trained a little younger as pulling is easier on their bones and muscles than carrying. Leaving it much past 5 means your horse starts to mature a little too much mentally and then they take, like older people, longer to learn everything.
Mules and donkeys/burros take longer to mature, and the muleskinners I've talked to recommend 5 for breaking and 6 for full work.