We hide the gifts and then put them all out the night before Christmas, after the kids are asleep. It just creates such a magical kind of feeling for them to get up in the morning and see all of those presents suddenly appear.
I will never forget the excitement I would have as a kid on the night before Christmas. Then I would run to the tree on Christmas morning and was always amazed at all of the gifts there. (There actually weren't a lot when I was growing up, but it seemed like it to me)
We always wrap all of the presents. The ones from Santa were in Santa wrap.
We found it was so much fun for the kids to unwrap the toys. There's always that moment of suspense when you wonder what is in the present.