An adult female horse is called a mare. Female horses under 4 years old are called fillies. In the context of breeding, a mare is referred to as the dam. Mares kept for breeding are typically called broodmares.
While adult male horses have different names depending on whether or not they have been castrated, female horses are rarely neutered, and, therefore, there are no distinctions made between an intact or a neutered female horse. Both male and female horses around 1 year of age are also referred to as yearlings, and newborn male and female horses are also referred to as foals.