It's a good question !
Britain’s decision to leave the EU also threatens the free movement of horses, potentially dealing a blow to the racing community in the UK and Ireland. A tripartite agreement between the UK, France and the Republic of Ireland allows thoroughbred horses to travel freely between those countries for races. Under an EU directive, the horses need only to have an EU passport and be on a livestock database. They do not require a veterinary export health certification or customs documentation. So, Brexit potential impact on the horse industry” will be important. We can't know what's going to happen.
Have a good day.