When I was young I picked up a book at a friend's house on astrology. I am a Taurus. I mistakenly opened it on another sign thinking I was reading the chapter on what made up a Taurus character. I was reading and nodding my head "wow, this is kind of weird. That is me. I do that. Well, I'm not like that but it's not going to be a 100% fit" After several pages I realized my mistake. And then I realized the Forer effect without knowing what it was or that it had a name.
(The background is she just found out she was actually born 3 months after her parents told her she was born - they lied to get her to start school a year earlier.)
Astrology is obviously nonsense, but it seems plausible that the season of birth could have a personality effect: the cold dead of winter, with little fresh food vs spring etc, also from the attitudes of surrounding adults.
Of course, different near the equator, and phase-shifted in the southern hemisphere, and... much less pronounced in modern times, with supermarkets, refrigeration, air-conditioning/heating, imported foods, and wider social presence (newspapers, TV, radio, internet, phone) etc.
There are actual studies. Lots of professional athletes were in the older part of their cohort when they were younger. So the effect Terr_ described seems to outweigh the one you describe.