Well, my experience with this involves a different holiday, but...
In 2003, during the High Holy Days, I'd just found out that my aunt had terminal lung cancer. (She died a couple of months later.) I had holiday cards to send, but many of them wished the recipients a healthy (Jewish) New Year as well as a happy one. I carefully looked over my cards and sent my aunt and cousins one that with a simple, subdued message as well as my father (my aunt was his sister).
I now wish I'd handled that differently...writing a heartfelt but not lugubrious note about how much they meant to me might have been better.