For a class size of 23 there's a 50% chance that two will have the same birthday. Sounds strange, but true, it's called the birthday paradox. Anyway, I have heard of schools here not doing birthdays since it means kids with birthdays in the summer will never get to have a birthday celebration at school.
My son has an August 9th birthday.
In his school (pre-school and kindergarten) they celebrated his, and the other summer birthdays, with parties during the last week of the school year.