Well, this can cause a lot of discussion.
For a business card, I wouldn't do that. Some of your customers will be offended perhaps or think you presumptious or whatever. I would stick with a more religion-neutral message. It doesn't have to be as uninspired as 'Happy Holidays'.
I don't blame people for pushing back on the Merry Christmas thing. I'm sure many disagree, but I am used to being in the minority on this anyways. So, from my minority viewpoint - I don't appreciate how many Christians (and other religions) want to make their version of their religion all pervasive and see nothing wrong with making our country into a religious theocracy. Everything is politicized these days. I will never comprehend how some people can claim to being persecuted while pushing to have their own view point embedded in every aspect of life on every street corner. One or more of your customers is bound to agree with me.
It's just push-back is all.
That said, I personally wouldn't hold it against you if you or your business sent me such a card.
Dave.