Dwight is wrong. The Romans celebrated birthdays. As an example, one of Propertius' most moving elegies is addressed to Cynthia in celebration for her birthday. The poem is a bit odd in that it's all Propertius imagining, rather than reporting, what Cynthia is doing, but he imagines her purifying herself and offering sacrifice and then speaks of her dressing up and banqueting, followed by drinking and birthday sex. That's just one (particularly cute) example, but there's really no shortage of references to private birthday celebrations in Latin literature. As early as Plautus birthdays were celebrated with feasting and conviviality, and in fact Plautus has quite a large number of very open references to birthday parties--in the Pseudolus the preparations for Ballio's birthday party are sort of of central importance, as they're supposed to be going on in the background while all the action happens