Read through any of the ante-Nicean church fathers who debated this question, and they all agree that Jesus was probably born sometime in spring. All the evidence, as little as that may be, points in this direction. However, you are right in your last statement. There's no real way to answer this question, and it all comes down to conjecture.
Two brief requests:
- Drop the pretention. The overwhelming majority of the "ante-Nicean" [sic!] never addressed the issue.
- see post 29