Does it make more sense that Jesus was born in late September or early october, and not December 25?

I believe He was born during the Fall season. I don't believe that Jesus was born during the Winter and especially not on Dec. 25th. I think telling people this is ultimately ... lying. If one chooses to celebrate the life of Jesus being born ... fine. I just think it should be made clear that it's not His birthday (Dec. 25th) we celebrate but basically that He was born unto us to save us from our sins.