I think you can find connections between anything if you try hard enough. The date of the celebration (December 25) is traditional, and is not considered to be Jesus' actual birthday.... it isn't in the Bible. It is commonly accepted that the date was chosen to coincide with the Roman winter festivals in the 3rd century AD. The Romans worshiped the sun gods on that day because of the winter solstice, similar to what you've described. So sure, it is definitely safe to say that many other cultural and religious factors came to influence the common perception of Jesus Christ. The most obvious examples come from Zoroastrianism in my opinion.
However, out of all of these previous religious beliefs and mythology that influenced Christianity, there is still one element (many would argue the most important element) that is entirely unique: Paul's theology of Original Sin, or the idea that Jesus sacrificed himself and died for humanity's sins. That isn't found anywhere else, Judaism, Zoroastrianism, or Roman/Greek and Egyptian religions.
Interesting article about Zoroastrianism's influence on Christianity:
http://www.sullivan-county.com/news/...oastianism.htm