We've decided to wrap and put "ours" under the tree ahead of time, put the unwrapped Santa ones out on Christmas morning, and to not wrap stocking gifts. I like the anticipation of them seeing the gifts under the tree, and I'm sure seeing the big gifts they asked for from Santa out when they come downstairs is going to be super fun.
We startd this exactly this year. Everything used to come out Chrsitmas eve but we look to see the excitement for a few days before with the wrapped gifts. We also make the difficult to wrap gifts from santa so we dont have to deal with wrapping them.