In the Xmas special, The Doctor's "home" was decorated with drawing supposedly given to him by the children of Christmas. I'm assuming that these drawings weren't made for the show by the art department, but are most likely drawings that actual children have sent to "The Doctor" in fan letters. Anyone know if this is the case?
No idea. If anything, I would assume that they are specifically created by the art department for the episode. That's what art departments are for. They seemed pretty uniform for them to be a collection of random drawings from child fans.
I wondered this myself. If it was only a single child's drawing (or two) as sometimes shown on an episode of a program like "Law and Order: SVU", I can see an art department handling it. Maybe the same was true for "Time of the Doctor", but I think given the nature of the show, its audience, and other 'promotions' asking for kids' involvement (like the Blue Peter contest to design a Tardis console for "The Doctor's Wife"), maybe school groups were asked to contribute and be a part of the show.
Imagine the joy of a young fan, seeing the drawing they sent to The Doctor, on television, and actually hanging on the wall of The Doctor's house! On Christmas!
I imagine they would be pleased. I still think the art department did them though. If children's drawings were sought from the public, wouldn't there be an announcement somewhere on the web?