The doctrine of the Trinity does predate Christianity, but not in the way you suppose, i.e., with origins rooted in paganism. There is no pagan equivalent to Trinitarianism. You will undoubtedly cite a number of tritheistic models and dub them for some kind of pre-Christian framework. But in reality, they do not run congruent or parallel one another.
You cannot even argue that "Christmas" (the birth of Christ) or "Easter" (the celebration of the resurrection) is rooted in paganism, because for one: You need to first establish that your prior Catholic convictions (that Jesus was born on Dec. 25) is actually the date He was born. In fact, the Eastern churches celebrate the birth of Christ on January 7th. And if you've managed to prove that Christ was indeed born on Dec. 25, then you have to prove that this was borrowed from a pre-Christian pagan cult.
There's a host of issues here: You assume your prior Roman Catholic convictions as the standard Christian belief, but wind up excluding half the Christian religion.
If you do not mind me interjecting into the conversation, I would like to point out a couple of things about the holidays.
First - Christmas does have it's early beginnings in the Roman festival of the Sun. This was observed on December 25th. as a celebration of the renewing of the Sun, as it came out of the winter season. Today it is known as The Winter Solstice, which will take place on December 22nd, I believe.
- Christmas was also incorporated into the early Catholic church, as the celebration of Christ Mass.
- Additionally, the Bible states, that at Jesus' birth, the shepherds were tending their flocks in the field at night. (Luke 2:8) This is not done in Israel during the winter months. The sheep would have been in the sheep pens at this time.
Second - Good Friday and Easter, are all wrong.
- During Passover - Friday would have to be the wrong day for Christ to have been crucified. First, because Christ Himself said He would be in the grave three full days. He gave Jonah as an example. Good Friday evening to Sunday morning is only 36 hours, not 72 hours. This is made even worse, by a fact that many overlook. The Jews measure a day from 6:00PM to 6:00pm the next day. Why? Because the Lord said the day started with the evening. (Gen. 1:5) Therefore, Jesus Christ would have rose just after 6:00PM Saturday. The Jewish beginning of Sunday. So understanding this, Our Good Friday would have Jesus in the Ground for just a little over 24 hours.
- There are other reasons why Good Friday does not work for the Crucifixion date and they have to do with the nature of the Passover "High days" and the regular Sabbath on Saturday. It makes for a great study - if you are interested.
Third - The Lord Himself, did not ask believers to remember or celebrate a date for His birth or His Crucifixion. He did however, command us to remember Him and instituted the Lord's Super until He comes, for this purpose.