For that matter, when did Christmas even become a celebrated holiday? I know that present-giving is from the three wise-men, but when did the Christian community take over the practice? Sorry for asking multiple questions in one post.
I think this question should be rephrased: When did people who celebrated a gift-giving holiday in mid-winter become Christians?
In Saturnalia, sigillaria were gifts exchanged during the last few days of the observance - wax or clay figurines, like so.
For Yule, according to Nigel Pennick (is he given much credence here?), pre-Christian folks would exchange baked goods and other edibles, gathering for shared meals. More respectably, maybe, the Heimskringla describes mass animal sacrifices and much sharing of their meat (along with goblets of mead) during Yule gatherings in 15, 16 and 19 of "Hakon's Saga". The sacrifices appear to be a kind of gift, and generosity is kind of a theme of the feast.