For domestic horses the answer is yes, no and maybe!
While it is true that wild and free living horses survive without rugs, they move more than their domestic counterparts and are able to find their own shelter from bad weather. On the down side, wild horses do not tend to live as long as domestic horses. Older domestic horses may therefore need extra warmth in cold wet weather but healthy younger horses do not usually need to be rugged especially if they have access to shelter (which all horses should have).
However some breeds of horses have a very fine skin and coat (such as Thoroughbreds and Standardbreds). This means that they feel the wet and cold more than tougher, hardier breeds of horse. There are always exceptions though so treat each horse individually.
Rugs should not be used as a substitute for shade and shelter (see the article Do I need to provide shade and shelter for my horse?).
Using rugs on horses in summer can be a welfare issue. Rugs do not keep horses cool. A horse naturally has a sleek coat which reflects the sun and a horse will seek shade when they are hot as a natural response. All large bodied animals, such as horses, take longer to cool down (and warm up) than smaller bodied animals. Rugs prevent any cooling breeze from cooling the body. Also horses are one of the few animals that rely on sweating to cool down and rugs impede this process (by preventing air from passing over the body, evaporating the sweat and cooling the body).
Many people rug horses in summer in order to prevent their coat from fading in the sun. If horses have access to shade they will utilise it in the heat of the day. If this is an issue for you confine your horse to shade through the day (in hot weather) with access to hay and turn them out at night. This is especially important for horses that have white skin over areas such as the nostrils and therefore get sunburned easily. It will also reduce the problem of insects for your horse because insects are not as problematic in shade and at night.
Horses that suffer from Queensland Itch, which is an allergic reaction to midge bites, do need to be lightly rugged in summer to reduce insect bites.
In cold wet weather a good quality and well fitting rug can help the horse to maintain condition, as a cold wet horse will burn a lot of energy keeping warm. Keep in mind though that if your horse is young and healthy but tends to get fat, rugs will actually help him or her to maintain that fat. In a natural situation excess body fat is burned off through the winter.
The coat of an unrugged horse stands up in cold weather to trap air and warm the horse. If you decide to rug you have to compensate for this mechanism as a rug will stop the hair from being able to do its job. In some circumstances a rugged horse is actually colder than an unrugged horse if it is a badly fitting thin rug that flattens the hair and reduces the movement of the horse without providing any real warmth.
Rugs need to be checked regularly (at least twice a day) to make sure that the straps have not broken and the rug slipped, which can cause injury to your horse. Hoods can be very dangerous for horses and should only be used if the horse is being checked very frequently (much more than twice a day) because if a hood slips it can cover the eyes and rub the eyeball (which can cause an ulcer on the eye – a very serious condition for a horse requiring immediate veterinary attention). Horses with slipped hoods (due to not being able to see) have been known to fall into dams (and drown), injure their eyes on branches or other protrusions etc. or panic and run through fences.
A rug should be removed regularly to make sure it is not rubbing, letting in water etc. and to make sure the horse hasn’t lost weight or gained too much weight. Rugs prevent horses from exfoliating their skin properly (by rolling and mutual grooming etc.) so a rugged horse must be groomed thoroughly and frequently to get rid of the build up of dead skin and hair.
For more information see: http://www.equiculture.com.au/horse-care-and-welfare.html
This information is from the RSPCA Australia Knowledgebase.