Astrology was developed thousands of years before our understanding of nutrition, internal medicine, obstetrics and fetal development.

At the dawn of civilization, people had babies throughout the year (obviously). Pregnancies proceed according to a consistent and predictable timetable. Due to variances in the food supply during different seasons, ancient mothers would not have eaten the same diet at every point during the year. Therefore, the nutrients being supplied to the babies in utero would have varied, and it's not unreasonable to imagine different babies' traits developing according to what food was available.

Ancient cultures would not have seen any of this. They would only notice that babies born at a certain time of year had a tendency to be like other babies born at that time of year, and unlike babies born at different times of the year.

They may have attributed it to the only outside factors they could see: the stars. So they made up stories of how the stars and planets control our temperaments, and the rest evolved from there.