Kind of dropped the ball on the url. days.to is great, but days.to/until/christmas is kind of wonky. I'd remove the /until/ part so it's just days.to/christmas
There's also a /since/ for each one.
A simple fix, use days.to/next/christmas and days.to/last/christmas. Clean URLs, and they make grammatical sense.
Originally, the site had exactly as you described with a cleaner url, but SEO had different ideas.
It would be extra cool if it considered each person's local timezone.
If you're counting to a date (without a particular time), you'll get the remaining time to midnight in your own timezone. If it's an event with a time, you'll see the start time of the event shown in your local timezone (but the countdown/remaining time will be same everywhere).