As someone who has sent “Happy Holiday” cards to clients - largely advertising, reminding them that you’re still around and still in business, that you hope they’ll remember you next time they need whatever you’re selling.
But also a genuine “thanks for the business”, or because they’re clients you genuinely like working with and have enough a connection with to want to include them on the annual holiday card list.
I don’t mind getting them from businesses (although “warm and fuzzy” might be overstating it - unless there’s a useful coupon enclosed!)
In my area the only businesses that seem to send out Christmas cards are the local real estate agents. I get so many flyers from them throughout the rest of the year that their Christmas cards have little impact.