Although greeting cards and Christmas seem to go hand-in-hand, people send cards for a variety of reasons. The holiday season, in fact, extends from Thanksgiving to New Year's. Business owners may take the opportunity to recognize their customers with business greeting cards and extend their best wishes when personal visits or phone calls aren't possible.
Whether or not you personally celebrate the Holidays by sending business Christmas cards, when choosing your company's holiday card it's important to think about your recipients. Unless you know for sure that they celebrate Christmas, it may be inappropriate to select a card that makes specific reference to Christmas. If they do celebrate, is it in a secular way? While it's true that political correctness can be just as controversial as the topics it covers, the bottom line is that the greetings you're sending to your customers shouldn't run the risk of alienating them.
Some people may consider "Season's Greetings" or "Happy Holidays" generic, but the idea behind such greetings is to spread holiday cheer; regardless of the recipient's faith or beliefs. Holiday Christmas cards with a Peace on Earth sentiment can be a good alternative to faith-specific or PC greetings; it speaks of a common wish encompasses all of us.
If your target audience is comprised of friends and family, you will likely have a bit more flexibility in how your message is accepted. Your college friend in Arizona probably won't be offended if your card features a winter scene with snow he hasn't seen since your days at Harvard (although, he may be a little jealous!).
Ultimately, it boils down to the "know your audience" rule. If you know your recipients would not be offended by a card that is religious in nature then it is perfectly acceptable to send them a card that celebrates the true meaning of Christmas as seen through your eyes.
You are the only one who can decide whether the message you choose for your holiday card risks offending the addressee, and whether that is a risk worth taking. Sending a greeting card should be a show of the connection between you and the person you send it to, and not a potentially bond-breaking action.