In all this discussion I think its important to note there are two types of "Christmas". Some people don't like that, but its a reality that can't be denied. There is the Christian religious holiday of Christmas which celebrates the story of Jesus' conception and birth and wise men and all that. But there is also a secular, totally non-religious, social holiday, which for clarity I will spell X-mas.
The two overlap a lot, but they are different. In this thread we've already head lots of examples of people celebrating X-mas, including the original issue, but also Muslim's giving gifts or Jewish or atheist folks celebrating generically. OP and her family might celebrate Christmas, but the snowflake gift was carefully chosen to be an X-mas gift. American's as a nation observe X-mas - its a national holiday, mail isn't delivered, public schools and banks, etc are closed, public transportation takes on a different schedule, etc. Plus companies have parties, employees and friends and neighbors exchange gifts and cookies and the like. People and companies decorate, as often as not with generic things like snowflakes and snowmen, or sparkles, or candy. Many of the seasonal songs are actually X-mas songs not Christmas (Jingle bells for example).
There are many Christians who are offended by this secular co-opting of Christmas into X-mas. The news covered "keep Christ in Christmas" issues and surely we have all encountered it on some level personally, whether it be a conversation or even just seeing a bumper sticker. The whole "Merry Christmas/X-mas" versus ""Happy Holidays" debate is tied into it. But for better or worse, good or bad, this is what has happened, in a widespread, mainstream way in the US. We have a totally secular, open to all, holiday that exactly overlaps with a major Christian holiday.
Its unfortunate the OP's daughter's friend's parents are taking such a negative and aggressive stance against X-mas, but it is what it is. They are entitled to feel that way. But I don't think they are doing themselves, or their child, any favors in the way they are taking this stance.
On the other hand, I think the OP is doing a great job in making sure her daughter understands that X-mas (or "winter break" and "snowflake decorations") is for everyone while Christmas is specific to certain people.