Honestly, I don't think their living arrangements have that much of an effect. Of course, it also depends largely on the safety of the environment the horse is in.

Where I used to board, horses were constantly getting injured. It was ridiculous, really. Yes, most of it was just small stuff, but if they owners of the barn had bothered to actually do upkeep (they NEVER fixed or did small repairs to the fencing yet they owned a fencing company, I mean wtf?!) most of the small stuff and without a doubt almost all of the major injuries could have been avoided. At this place, one horse was in a fairly large run with a 3 sided shelter, and the other was in a stall (with no turnout, NOT my choice.. I turned out in the arena as much as possible, and one of the elevently trillion reasons why they were moved).

Where my horses are now, the owner is soooo good with keeping everything super safe, my horses have had almost zero injuries in the 4 years they've been here. The one injury other than minor hair scrapes was when my mare sliced up her tongue last year, but that was all her fault and had nothing to do with her environment (she's not the sharpest crayon in the box). Here, both have a stall with attached run. One has 27/4 run access, and one is 12/12.

"Who leaves a country packed with ponies to come to a non-pony country?" - Jerry Seinfeld