I think most people would know what you meant if you said Yule. :) I'm a little iffy on using "Christmas" to describe what I celebrate as well, as I too am not Christian. But what I do celebrate is very Christmas-like, just only with the secular traditions, and we don't do it actually on Christmas day.
We have a pretty normal Christmas celebration at my grandma's house with my large extended family on Christmas eve. With the other side of my family, it's usually just a nice big meal with family, which is also lots of fun. At home, my mom celebrates Winter Solstice. She gets me gifts if she can, but we came up with a fun tradition of our own where she hides one around the house each day and I have to find it. But we have some very christmas-like decorations like a ceramic christmas tree (they're even prettier in person!) and... I put tiny christmas ornaments on my asparagus fern. :lol: So... christmas-type-thing!