At our barn most horses wear a rain sheet either light or medium. Blanketing is not done for warmth, but to keep them dry and from getting dirty. It is up to horse owners to provide blanket and if they want it off or on at certain times it is up to them. BO/workers (including myself) check for loose straps at feedings and cleanings. Most of the horses are in run-in shelters with small paddocks so they all have access to the elements. The weather can be 50 and raining (this weekend) or 30 and snowing (last weekend). Horses all have fluffy winter coats right now. If someone notices a tear, the policy is that the blanket comes off.
It's sort of a family there and everyone looks out for each other. A couple of the younger boarders have been given blankets for their horse because they couldn't afford to buy one, and if someone has a hard time coming out for whatever reason, it's not uncommon for another boarder to take their horse out once a week and give them a good brushing, or fix the blanket. It's what makes this barn so nice.