If you meant something more literal or biologically focused (e.g., horse mating behaviors in zoos, or human–horse romantic narratives as fantasy fiction), please clarify. The above treats the topic as suitable for a general audience.
Stallions are used for breeding and can breed multiple mares during the breeding season. Zoo Sex Animal Sex Horse
The natural breeding season for horses in the Northern Hemisphere is from early spring to early fall. If you meant something more literal or biologically
Many regions have regulations around horse breeding, including licensing of stallions and registration of breedings with relevant equine registries. horse mating behaviors in zoos