If the last time you saw them was the last day of term, they're not friends.
This. You're confusing 'people I see a lot of because of similar routines but do not see outside those routines' with 'actual friends'. Talk to your actual friends about bad news, not to people who are standing in the playground next to you keeping an eye out for their child and wondering if they left the oven on.
I'm quite fond of some people I see on the school run, but I never think about them unless I see them, and I never see them unless our paths cross in relation to a school event.
Sorry to hear about your dad's diagnosis, OP.
My DF died on Christmas Day 2008 after being diagnosed just 2.5 weeks prior. You’d think in that case people might say something nice at Christmas time but really people only care about themselves.
I'm sorry for your loss, @AhoyDelBoy, but think that's rather unreasonable as an indicator of friendship. Unless you remind them of it, and/or your friends are the kind of people who are very conscious of anniversaries, significant dates, birthdays etc, I don't think that remembering the date of death of a friend's father ten or eleven years on is something a lot of people would remember unprompted, whether it's Christmas or not.