Every so often I run across a Christian that is appalled that Christmas and Easter have pre-christian pagan roots. They are angry that the church does not denounce those holidays outright. They tend to be contemptuous of fellow Christians who observe those holidays. After all, aren't Christians celebrating paganism by doing so?
Short answer; No.
Yes, celebrating Winter Solstice and the coming of Spring do indeed go back to pre-christian, pagan times. But don't get your exercise jumping to conclusions. Primitive people celebrated the coming of Spring because of the rebirth of nature after the bleak months of winter. Did you think it was a coincidence that God set the resurrection of Christ at the dawn of spring? Hardly. As C.S. Lewis put it, myth became reality in Christ.
Christmas is a bit harder to grasp because everyone knows Jesus was not born in the winter. Moderns won't like this, but the ancient world just was not as pedantically concerned with the precise measure of time as we are. There was an existing pagan holiday--Winter Solstice. Why not have people celebrate the birth of Christ, instead of the death-like nature of Winter?
The fact is, what the early church did was to take existing pagan celebrations and fill them with Christian meaning. Over time, the pagan message was mostly lost and the Christian meaning reigned. Think not? When is the last time you worshiped Astarte at Easter? Nobody celebrates those pagan meanings anymore. They have been redeemed. ...Sort of like what God does with pagans who surrender their lives to him.
Modern Secularists have learned from Christianity. Over the last forty years they have worked hard to strip Christian meaning from the holidays. Our schools no longer celebrate Christmas or Easter vacations, instead we have Winter and Spring break. Secularism seeks to strip the Christian content just as the church once overthrew pagan concepts. And its working, too.
Secularists would like us to believe this is perfectly normal. That it's in fact what the Founding Fathers envisioned from the start. But that is not true. The Christian holidays of Christmas and Easter were enthusiastically celebrated by Americans for over two hundred years. In my own school days we sang evangelical Christian songs at school plays and concerts. It was considered a part of American life.
There are still a lot of Christians in America. We still celebrate the Christian meaning of those holidays. But the culture seems to be passing us by. I don't think crying foul and recalling that we are a "Christian nation" is going to change the current situation. The right thing for believers to do is to glorify Christ no matter what the culture does. That's what they did in Roman times.