Astrology is obviously BS - but being born in summer or winter must make a difference for kids! It's the difference between spending important periods of your life totally bundled up, or running around freely.
There are definitely stages in human development which happen at predictable times - 1 year for first steps, etc, and the variation in the schedule is usually less than a few months - small enough that birth season could matter. So winter babies go through stages together as a group at different times of year from summer babies.
If we lived on a planet which had longer years, this would be much more pronounced. If a year were 4 Earth years long, a season would last a year. The season you were born in would make a huge difference to you. You'd have more in common with co-seasonals - people 4 years younger or older than you - than with people just the same "age".
You might see winter for the first time at age 2, or age 4! On planets with even longer years, you might spend the first 10 years of your life bundled up, then the next 10 sweating. Those cycles could have reprecussions on the culture as a whole. 80s nights would be categorically different than 70s nights, due to differeing weather in that decade.
It seems like there should be a way to pretty easily prove or disprove the simple version of astrology: for whatever characteristic that someone claims is related to astrology, look at the data for people in Australia, and see whether the data matches up better as is, or shifted 6 months off.