Yes, like you, I have a ritual where I go out on Christmas day.
Normally after dinner.
What I do is ask everyone if they would like to come along as well. I do that to seem friendly and sociable, but every ounce and fibre of my soul is hoping that no-one takes me up on the offer. It's my chance to get away, recharge my batteries, have a bit of solitary time before going back to the sound and fury of a family Christmas afternoon and all the boisterousness that will involve.
To date no-one has taken me up on that offer. Not sure if that's because they know I want that time on my own or just because they don't fancy it. Knowing my family, it could be either of those. The day someone says 'yes' I will whither inside.
On New Year's day I go out for an early, sunrise, walk. I make believe that it's just because I fancy getting out for a bit because I've been inside for the last few days on what is normally grubby weather that time of year. But in reality it's so I can watch the sunrise on a new year and reflect and enjoy watching it come up. Not sure why I haven't confessed my true motives. I suppose I like a bit of personal secrecy, I think that can be important. One doesn't need to share everything.
On a personal level, I make it a point to always make sure I personally say 'happy Christmas'/'Happy Birthday' etc to people because I never send cards. My personal feelings are that if you need a card to express your wishes then your probably don't really feel them yourself. That's my position, not suggesting everyone feels the same or should. So because of that I like to ensure I say it direct to them, ideally in person if I can, but a phone call if not (e.g. due to distance), as a sign that I genuinely am wishing them well. It's important to me.