It is necessary to vaccinate your horse. Among the general vaccinations, some of them are compulsory and others are advised. The flu, the rabies or even more the tetanus. Poloconsult gives you more details on your horse vaccination here.
The compulsory vaccines:

The rabies vaccine, in case the horse is in contact with the public or if it participates to some tournaments.
The flu vaccine, if the horse participates to some sporting events or travels a lot.
This vaccines are recommended to prevent some serious diseases and can be administrated at any age.

The advised vaccines:

The tetanus vaccine is not compulsory but highly suggested due to the presence of the germ in the horse environment.
The rhino pneunomia is also recommended, when the horse is surrounded by others animals.