What sort of activities did your child's school do for the "Christmas" holiday?
My 12 year old is in a public school and they keep things pretty neutral, they do sing holiday songs but most are the less religious ones. They have a little party at the end of the week, the theme seems to vary with the class, younger ones parties are less religious.
My 2 year is in a private school and activities vary with the teacher, I was very happy with her teacher this year. They were taught about multiple religions and what they celebrate this time of year. They had a big party on the last day which was just a celebration with friends, they sang pretty neutral songs and played fun games.
Being an agnostic I like that my children get exposure to religion, it gives me a chance to talk to them about it and state my reasons why I haven't chosen any path of faith.