This seems like one of those obvious ideas, but I'm still feeling all clever about it.
I had a cheap (under $2) box picture frame, basically a clear plastic tray with a white cardboard box inside to go behind your photo. I decided that the white box looked kind of dull.
(this is the back side)
So I got out some of my Christmas gift wrapping tissue paper -- a metallic gold -- and wrapped the inner box like a present.
The tricky part was putting the wrapped box back into the frame, because the tissue paper rips easily and the box fits pretty snugly in the frame. I just did it slowly and carefully and managed to get it back in with no damage!
Much nicer than "cardboard white"! That's my niece, by the way.
I only taped the tissue paper to itself, not to the box, so I could always rip the tissue off and put in a different color. You could change it to go with your seasonal decor! Given how snugly the box fits in the frame, though, I'd be worried about going with any paper thicker than tissue paper.