There's a good reason for this. A safe anesthetic for horses did not exist until the 1980s - I actually remember the first one being invented. General anesthesia in horses is also risky - they are inclined to injure themselves when they go down and again when they get back up (They often freak out in recovery). They may also injure assistants or handlers. Post-operative colic is also common.
Because of this, major surgery in horses is avoided as much as possible. If it's at all possible to do a procedure under local anesthesia plus sedation...
Spaying is generally not considered worth the risk unless there is a genuine medical reason for it or the mare has such bad "female symptoms" that she cannot be used or worked. Laproscopic spay has been developed for use in horses within the last five years, but very few vets are trained in the technique.
So, no, mares are rarely spayed. Gelding and proper handling of stallions is relied on for population control (Of course, surprise foals do happen after stallions get over the fence and almost every long-term horseman has some story about arriving at the barn to find they had one more horse than they thought they did), and other methods such as herbs and drugs are used to control heat-related behavior.