Horses CAN get "splints", but not what I would consider the same thing as human shin splints. The splint bone is a residual of one of the 'original' multiple toes that the early forms of horse had; it lies along the side of the inside of the front cannons, coming down from the 'top'of the cannon, and sort of tapering off to 'nothing'. It is usually a impact to this area, but anything that causes inflammation there can cause a 'splint' to form(this is the main reason why people use splint boots on their horses' front legs, even on minis.) A 'splint', which is a calcification, creating a hard, vertically linear enlargement over the splint bone(meaning, relatively high along the inside of the cannon bone) may be painful when forming, usually isn't once it is 'done'. Splints can be removed, if you do it when it is 'fresh'-I have done it, years ago. Though it is not impossible for ground concussion to cause a splint, it is most likely to be caused by a direct impact to the area. I have never seen a mini with a splint-there are probably a number of reasons(one of which is that lots of people do use splint boots regularly), but I would postulate that major ones are that minis aren't used in vigorous pursuits where hooves are more likely to make hard contact with the inside of another leg, like reining and cutting, and the fact that their body weight is relatively light. As for seeing them on (full-sized)performance horses-I have to say that it is likely to be a combination of the tendency to use them TOO HARD, TOO YOUNG(basically, as VooDoo said)---AND, the way many modern stock horse breeds have been bred-to have pasterns that are TOO STRAIGHT, and feet that are TOO SMALL! -that is responsible for many horses having them.
ANY horse, whether big or small,needs to be trained/used in a way that does not OVERstress its physical components, especially those relatively delicate legs and feet-there is no muscle below the knee and hock on horses-only tendons, ligaments, and bone-all structures that if injured, are difficult, and SLOW, to heal. This is why it is SO important to try to first, breed them to have correct components-strong, short, dense cannons, pasterns of proper length AND slope(no 'extremes, either way) and good feet-strong, round, BIG enough to properly support THAT horse, with quality horn and proper structure-good wide frog, open heels, etc., etc. THEN, you allow them to develop and mature without overfacing body structures(not to mention their minds!) until they are mature enough so that the physical demands of training/performing aren't likely to present undue risk! IN MY OPINION-there is 'way too much 'rushing' of horses in this country into high level performance events of various sorts-look at horse racing, and at the multitude of 'Futurities'-Good for someone's pocketbook to win, BAD for the horse's health. It seems to me that there is a philosophy that you can 'push' one early, and if you 'use them up' early, why, just throw that one away, and get another. Horses shouldn't be unsound by age 5 or 6!
OK, off my soap box! All that said, I occasionally trot my horses on a nearby pavement(subdivision.)Usually,they're wearing Easyboots-then-not often, not all that far-and according to their age, level of training, and most importantly, level of conditioning!!