Was Jesus really born in December?

I have been told the Christmas story all my life--not the one in Luke (although that was read to us every year at a Forreston school assembly by the principal, John I. Masterson), but the one about how Jesus wasn't really born in December and the early evangelists used that story to coincide with the winter solstice celebrations. Taylor Marshall says that is a myth that began as a polemic against Christianity to question the historicity of biblical Christianity. In 2013, he wrote a book about it, and you can download it. "God's Birthday; why Christ was born on December 25 and why it matters." Saint John Press, 2013.
 https://www.dropbox.com/s/z0fpjv5ttmm4knc/God's%20Birthday%20text%20Dec%2017.pdf?dl=0