Equine gestation is about 11 months. Anecdotally, draft mares tend to have slightly shorter pregnancies.
Horses breed in the spring or summer. The normal cycle is that the mare comes into heat about a month after giving birth and, if all goes well, conceives and gives birth in 11 months - thus, one foal a year, about a year apart. (Horses can conceive twins, but I'll talk more about that later).
Horses are harem breeders - meaning a group of mares is bred by one resident stallion who, under normal circumstances, keeps those breeding rights strictly to himself. It's probable that mares occasionally sneak off and are bred by a different stallion - this happens in most harem breeding species. In some cases, two stallions may work together to keep their harem. (Other harem breeders include lions and elk).
A mare will come into season about every 3-4 weeks until she gets pregnant, but only comes into season during the summer months. This is triggered by day length, not temperature. Mares generally don't look pregnant until fairly close to due - many is the story from horse people, often with decades of experience, of getting a surprise when the first they knew a mare was pregnant was when they had one more horse than the previous day!
It's even harder to tell with mares that have had several foals...their bellies don't always return to a nice flat state afterwards.
A few days to a couple of weeks prior to foaling a mare will "bag up." That means her udder becomes full and swollen and there may even be some leakage of milk. When foaling is imminent, the muscles of the tail and croup relax noticeably. The mare becomes restless and may paw the ground, pace, and stare at her sides - probably an indicator of feeling contractions.
Horses can actually control the onset of hard labor! A mare will not give birth if she knows there are predators around or if she feels threatened. In the days before close circuit cameras, mares were notorious for waiting until their owner stepped out to get a cup of coffee and giving birth in their absence - even a trusted human still counts as a predator.
Once hard labor begins, the mare will go down onto her side. The foal, like most babies, comes out head first, nose on top of hooves. Horses get it done quickly - if the foal is not out within twenty minutes of the mare going down it means there are complications - more on that later.
The foal is born with little soft caps on his or her hooves - this prevents the developed hooves from damaging the uterus or vagina. Foals stand immediately and suckle as soon as the mare is finished with the afterbirth and on her feet. (They often fall over a few times to start with, but the instinct to stand is very strong).
A wild foal will stay with his or her mother until the next foal is dropped, at which point they are driven out of the herd completely. Colts join all-male groups called "bachelor bands" - fillies are generally welcomed by a nearby harem. Unlike many other harem breeders, both sexes are expelled - this way a strong resident stallion can stay with the herd for several years without covering his own daughters.
Domestic foals are generally weaned at about six months - more on that later.
A domestic breeding herd of several mares and foals in Iceland. This was August, and the mares either had newborns or were heavily pregnant - Iceland has a brief summer and foals are born at its very peak.