Horses are all individuals, just like people, so they have different needs.
I have known some horses be very settled in 24/7 BUT and this is a huge 'but', they were ridden daily, they were put in the horse walker twice a day and in addition hand grazed twice a day. This kind of care is usually not available in most yards as it is extremely labour intensive.
Most horses do better with as much turn out as possible. It gives them a chance to run around, expend some energy, socialise with other horses and, very importantly, eat continuously with their heads down (this helps digestion and avoids problems like colic and ulcers). Ideally horses should have forage 24/7, so in the winter when there is no grass you should supplement with hay in the field. If the horse puts on weight easily you need dry hay of low nutritional value, if the horse is on the thin side you may need do add haylage and/or hard feed.
Many horses can live out 24/7. This depends on a number of factors such as whether they feel the rain/cold, whether they have field shelters or natural shelter in the form of trees and hedges, whether they are clipped, etc. Native breeds are usually quite hardy and can live out, if you have something like an Arab which is bred to deal with extreme heat, it may need stabling at night. In general if you see the horse losing weight and more food is not helping you may need to consider stabling. If a horse is fence pacing or standing at the gate neighing, it may be telling you it wants to come in.
It is worth having a back up stable even for horses that live out 24/7 so that you have a dry place to groom and tack up, as well as somewhere to stable them if they are ill.
To keep horses turned out you need suffient acrage. The BHS recommends 1.5 acres for the first horse and 1 acre for every horse thereafter, but it varies wildly with the conditions of the land. For example, in clay soil you may need a lot more land, fenced into a lot more paddocks to avoid poaching by the gates and well used areas. Grass does re-grow in spring but if the field gets terribly trashed it may need re-seeding and resting. Some yards have a 'trash paddock' for very wet conditions that gets sacrificed to save the other paddocks for spring when the grass returns.
The conditions mentioned are preventable or treatable. Rain scald is rare and if your horse has a rug on it's not an issue. Mud fever is common but if the yard has hard cored gates and well managed fields it may not be an issue. There are also many products out there that keep legs dry or treat mud fever. Weight loss can usually be managed with more feed.
If you keep a horse in 24/7 you need to manage all the accumulated energy. You may have ridden problems like running off in canter, jogging, rearing or bucking, and you may have handling problems like pulling away, rearing, and just generally feeling too full of life! It all depends on the amount of work you do with your horse, the amount of energy you put in (feed) and the amount of energy you let them expend naturally (turn out). Get the balance right and everyone is happy!