Will you be doing this in front of the family? Or were you planning on time away from the group for this moment?
I'm just thinking whilst writing, but I would think if you did it later in the night, there'd be a better chance that it wouldn't be QUITE as crowded, as many people with little ones will have started heading back to their rooms.
I also don't know if you wanted to do it up big or not.
I didn't do it in the MK, and I did it "halfway big." I proposed at the Rose and Crown in Epcot, a few minutes before Reflections of Earth. We had an outside table, and I had flowers delivered to our table as a precursor to my little lovey-dovey-make-me-the-happiest-man-on-earth speech. I would think something that's KINDA low-key but nonetheless sweet would be to do it before the fireworks, ask her what she's like for the holidays then slip on the ring when you explain what YOU'D like for the holidays is a life with her.
If you're able to peel yourself away from the family for the big moment, you could also consider a romantic dinner BEFORE the MVMCP. Bear in mind, while the party "officially" starts at 7, your tickets grant you park entry starting at 4. The rest of the family could go to the parks, and you could have an earlier dinner at Cali Grill or Artist Point, have a nice special dinner, pop the question, and then monorail or ferry back to the park to (hopefully) celebrate the answer AND the season with your family.