I'm an American and I send out Happy Holiday cards. This because I'm sending them out to Christians, Jews, Pagans, and atheists. And that's just my blood relatives. One card fits all categories. If they are lucky, the cards arrive before New Years since the USPS is unreliable.
My elected officials also send out Happy Holiday emails for the same reason.
December doesn't just have Christmas, it has Hannukah, the Winter Solstice, etc. In my experience, even atheists like to spend the December holidays with their non-atheist loved ones and like receiving cards.