keep them behind a gate
They just don't know how to be patient. The rule in my house is if someone sees their present, it goes back to the store.
keep them out of reach, until you want them to open them.
I'm having the same problem with my ant eater and donkey.
They don't know what wait til' the 25th means!
Curse those vile animals...........I'm gonna ground anty and gimpy!
I never trained them to recognize and open gifts to begin with...