All thoroughbred horses celebrate their birthdays on the same date. In the Southern hemisphere the birthday date is the 1st August in the Northern hemisphere it is the 1st January.
The reason they all have the same birthday is so that their ages can be standardised for racing. This is why it is important to have a foal born as close to the 1st of August as possible. Horses born in late November and December can be disadvantaged as they are severe months younger but have to compete in the same age group.