Our DS will be just 2 by Christmas and we haven't started any traditions yet - he passed out on the sofa just as lunch was served last year!
How about:
Making Christmas biscuits (can be a simple recipe to begin with) with festive cookie cutters.
Making paper chains.
Stringing together popcorn (looks much nicer than it sounds!), then eat leftover popcorn with a film: Charlie Brown's Christmas, Elf, Muppets Christmas Carol, Polar Express... etc.
Put bubble wrap on the floor and DC walk across it in socks trying not to pop any!
Track Santa on NORAD www.noradsanta.org/
Go for a walk, collects leaves, stick to paper in the shape of a Christmas tree (or something!)
Go see a church nativity somewhere - you don't have to be religious to enjoy one, and churches are so quiet compared to shopping and seeing Christmas lights!
Walk around your neighbourhood looking at neighbours' lights (you might have some 'enthusiastic' decorators.
Are you crafty? You could make cards or wrapping paper (potato printing, handprinting etc).
If you're low on budget www.frugalfamily.co.uk is a great place for inspiration.
When I was small we had a pillowcase full of presents (just one from the airing cupboard) but no stocking. My DSis and I got left one little present on our bed for opening when we woke up as we weren't allowed out of the bedroom/downstairs until mum/dad got us. Didn't bother me then and doesn't bother me now.
I'd like DS to have a small gift on his bed, stocking with us all piled in our bed together (stocking gifts don't have to be wrapped!) and then main presents after lunch. We may bend on the 'after lunch' rule when the time comes, though!
I'd definitely second pp about: walk in the evening in the cold, look at the stars and see if you can guess which one is the brakelight of a sleigh
then home, dinner, bath, pjs, film/book, hot choc (depending on age). DS has a fabric Osborne Christmas book www.usborne.com/catalogue/book/1~b~BCB~1303/christmas-cloth-book.aspx it has shiny bits, crinkly bits, soft bits, furry tails and a rattle on the Santa Claus page - he loves it!
Wow, long post
enjoy your Christmas 