A serious consideration here - if you send out cards, be aware that HP is also likely to as well. And because he seems so involved in his new love, he will undoubtedly use Christmas cards as a way of breaking the news to people - "Be happy for me! At last I've found the true love I've been searching for all my life," or maybe "Merry Christmas from me and my new chick."
Whatever he does - you don't want to get caught up in a lie by ambiguously sending a card from "Karen, HP and family".
Something we do - I create a card on the computer. For the 'cover' I use a photo we've taken, sometimes of the family and sometimes of something important to the family, such as the view over the sea from the cliffs near our house. Inside I put the usual Christmas greeting with our names (or "the Marg family"). But this is printed on a sheet of paper designed to fold in four to make the card. If you COMPLETELY unfold the card you get a letter giving news of us all. For some old friends, it may be the only news they get of us all year.
Alternatively - I email both the letter and any photos (including the cover). I might email the card as a pdf file.
Some years when I'm short of energy or enthusiasm, I only print a handful and send them just to immediate family. Sometimes I print dozens. But I always include our contact details so if they want to use the letter as a springboard to a phone call, the way is open.
You could be honest but tactful. Brief. "HP & I have separated a couple of months ago. He is living at [give his address] and I am now living with easy child at [give as much or as little info as you want]. We are selling our various assets but I'm still managing the paperwork of the business for now. Things are still very new, we're both still adjusting each in our own way. I didn't want you to find out via the grapevine so I'm using this opportunity to let you know.
[Add in any other non-HP news, the nice stuff, the happy side of things].
I'd love a chat with you sometime. I hope you have a really enjoyable Christmas this year, I am thinking of you."
Or just print it out and tuck it into a shop-bought card, for the easy option. You don't need to give details, just the facts, ma'am.
Because if HP is in any way inclined to shout it to the world, Christmas is HIS opportunity to tell it HIS way, noisily.
And the process of thinking of the nice stuff to put in - it will make you feel happier about your life now and where it is going.
Whatever you decide to do - be OK with it. All I'm doing is throwing another possibility into the ring for you to consider.
Marg