Origen writes about birthdays in a couple of places of which I'm aware: here is one place:
For Herod having laid hold on John bound him and put him in prison, not daring to slay him outright and to take away the prophetic word from the people; but the wife of the king of Trachonitis — which is a kind of evil opinion and wicked teaching — gave birth to a daughter of the same name, whose movements, seemingly harmonious, pleasing Herod, who was fond of matters connected with birthdays, came the cause of there being no longer a prophetic head among the people. And up to this point I think that the movements of the people of the Jews, which seem to be according to the law, were nothing else than the movements of the daughter of Herodias; but the dancing of Herodias was opposed to that holy dancing with which those who have not danced will be reproached when they hear the words, We piped unto you, and you did not dance. And on birthdays, when the lawless word reigns over them, they dance so that their movements please that word. Some one of those before us has observed what is written in Genesis about the birthday of Pharaoh, and has told that the worthless man who loves things connected with birth keeps birthday festivals; and we, taking this suggestion from him, find in no Scripture that a birthday was kept by a righteous man. For Herod was more unjust than that famous Pharaoh; for by the latter on his birthday feast a chief baker is killed; (Genesis 40:20) but by the former, John, than whom no one greater has risen among those born of women, (Matthew 11:11) in regard to whom the Saviour says, But for what purpose did ye go out? To see a prophet? Yea, I say unto you, and more than a prophet.