I would like to acknowledge first of all that while many elements of Christmas date from pagan traditions, the celebration that has been held in the West and the meaning it possesses is deeply embedded in Christendom. Whatever way you look at it, the holiday of Christmas is full of religious depth and meaning, and while some secular traditions are fun and enjoyable, I do not believe that it is right or profitable to secularise the day. Christmas loses the point.
I was once an atheist, and during that time, I did the Christmas thing but I didn't really think about it. I never gave it much thought because it was simply a cultural tradition - I failed to see what meaning it had and only looked at it from a selfish perspective (though ironically, I only enjoyed the religious carols - I still dislike carols such as Santa Claus Is Coming To Town, and for exactly the same reasons as before). I think, if I were still an atheist, I would continue to celebrate Christmas, but as an expression of cultural heritage. Now, I at least try to celebrate it for the deeper religious meanings in which I believe, though I'm the first to acknowledge that I spent very little time at all thinking about any of that.
I simply don't believe you can secularise the Christmas tradition and remove the cultural heritage from it. It becomes a worthless celebration of consumerism and materialism. Without the Christian belief that has given Christmas its meaning, it becomes a day on which you give people presents under social obligation - let's be serious, you could give people presents any day you wanted; you don't need Christmas to make you. A secularised Christmas is essentially a "buy things, give them to people, and selfishly expect presents for yourself" day. It has no serious worth, no point, no deep or significant meaning. It's a day of materialism, laziness, and eating. It is not a special occasion.
Keep the religious significance in Christmas. You don't need to believe it, you just need to acknowledge the cultural heritage and observe the worth of the day. After all, it is held to celebrate the birth of the most influential figure in history, and regardless of one's religious affiliations, you have to agree that Jesus Christ totally changed history's course. It's your subjective opinion as to whether it was for the better or not.