When we were young, a big tradition was to open one present on Christmas Eve. We still do that--somewhat. We usually all aren't together on Christmas Eve now that my siblings have their own families. But now it is more just the kids that do it.
Another is a Christmas Eve dinner of Ukrainian food. Cabbage rolls, perogies, borscht. This has pretty much not changed as long as I can remember, although who is at the dinner often varies from year to year. Everybody is welcome, especially friends or friends of friends who might not have anywhere else to go on Christmas Eve, so you never know who will be there. Which is part of the fun of the dinner. My mom usually also makes a ham or roast for those who might not be as enamoured with Ukrainian food as most of my family is.
My family also celebrates Hannukah so depending on when it falls, we have some weird hybrid celebrations when it overlaps with Christmas.
An annual match of Trivial Pursuit is also always a part of either Christmas Eve or Christmas Day. This is taken very seriously by some in my family (too seriously by a few and I include myself in that group), especially when the booze flows. Once that is over the table top hockey matches begin...
PS I like your tradition Bernadette. We have something similar in that my family.
"Don't be silly, Toto. Scarecrows don't talk. "