Mithra, the sun god of the Romans birthday was dec 25th
http://en.wikipedia.org/wiki/Mithra
Mithra is Persian in origin, not Roman. It is part of the Zororasrian pantheon and likely is not a sun god of any kind since Zororasrianism has a separate solar god.
Also, if Mithra’s birthday was December 25, why is the 16 day of the 7th month in the Zorastrian calendar dedicated to him?
And as far as I know Mithra didn’t make much of an appearance in the Roman Empire until after Christianity was already on the scene.
according to scripture Jesus started his ministry at about age 30, he died 3 1/2 years later in the spring at Passover..
Scripture says nothing to clearly indicate how long Christ's public ministry lasted. There is some speculation that it was only 1 year.