There is, as far as I can see in the legislation, no requirement for those few lines of programming to be written, not only for horses, but for livestock (thinking of the New Forest, Exmoor, other moorland and common land grazing areas), dogs (and cats!), and wildlife from deer of all sizes to swans which mistake tarmac for water.
A study from the University of Sydney
https://arxiv.org/html/2507.16258v2 found that most research and development work on autonomous vehicles (and autonomous robotic delivery vehicles) look almost exclusively at human conditions and requirements.