Short answer is no. A horse is a horse is a horse.
Grain & other high starch/sugar feeds are generally not good for horses. Some horses & types, be it due to being overweight, insulin resistant, the type of horse, etc, are more sensitive to the problems this sort of feed causes than others in this regard.
Lucerne/alfalfa is low in sugar but high in energy. It is also very high in calcium, phosphates, protein & nitrates, so while it can be a great feed, it should be fed only as *part* of a balanced diet, or else it will cause imbalances. Being high in energy it should also be fed sparingly to 'easy keepers', of which drafts often are.
Perhaps also the 'string' horses were getting a lot more work, so needed more calories than the drafts? Perhaps also they were from the same genetic line & susceptible/allergic to same things?
Colic is generally(not always) related to diet & how they're fed. Eg. Horses are evolved to 'trickle feed' - little & often - on low grade(compared to 'improved pasture & rich 'hard feeds') forage. Feeding rich feed, &/or in large &/or infrequent meals leads to all sorts of problems, including digestive ulcers & colic. So it may have been 'just' stress induced colic, but probably more likely that was the trigger or final straw, not the cause.