It was moved to winter to replace a Roman holiday. The solstice is on a different date. The seperation of church and state was only meant to prevent an official religion from being established and persecuting the others. Values from almost every religion were incorparated into the constitution. Don't kill, don't steal, don't attack anybody, plus more, are all values of Christianity and other religions. And because Christmas's main focus is no longer on religion, but Santa and presents, it does not even come close to enforcing religion on anybody.