The Centre for Alternative Technology has blogged about the waste behind Christmas presents. They're absolutely right that, even if you accept that Christmas is going to be about increased consumption, there's far too much overconsumption at Christmas time: consuming above and beyond what you need to in order to have the good time you're after.
A lot of their advice seems to be along the lines of "if you're going to buy something, buy it from our shop." Which is fair enough, if you believe that your shop is the most environmentally aware shop in the country: my guess is it might be, although it's easy even for green enterprises to be non-green when it comes to culturally acceptable practices, especially in terms of postage and packing. I'd love to know how they handle that, and how they work towards close inspection of their own practices.
Speaking of culture, though: wrapping paper remains undiscussed by the end of that blogpost. Which again is fair enough if you're talking about the CAT as a commercial enterprise; but that doesn't stop it being the rustling elephant in the room under your Christmas tree. The post doesn't really tackle it, unless it implicitly proposes you get all your presents delivered directly with a "do not open until Christmas!" label on them and just in brown paper.
There's a huge cultural pressure against unostentatious gift wrapping. My family is predominantly working-class, and their shared culture is just something I don't understand: much as mine is one they wouldn't understand; they'd blanche if I tried to give them presents wrapped in, say, magazine- or newspaper. They'd probably think it was something weird and posh that I'd picked up down south, which isn't far from the truth.
The main problem with plain wrapping remains the sheer boringness of it, when applied to a festival like Christmas that's meant to be about aesthetic excitement and bright colours. A reusable compromise, still with visual impact, might be something like the Japanese Furoshiki tradition, where fabric is used instead of paper.
This entails its own problems, though: the gift's recipient then has a square of fabric that they have to decide to do something with. If they bin it or even recycle it, then the embedded carbon lost is far worse than if you'd used thin wrapping paper in the first place. It's also a lot more faff than paper, and again, I can't imagine my family reacting well to something like that; although I wish they would!
Ideally it would be easy - and acceptable - for us all to have post-Christmas retrospectives of what resources we'd consumed, and when and why; that way we could take steps the next year to modify our behaviour. But even when so much recycling involves separating things out according to material, there's still that - again cultural - pressure to not look to closely at what you've already decided to throw out. Especially when it's the tinfoil at the bottom of the landfill bin, covered in week-old fat.