I've never heard that one. I'd have thought that "so don't I" meant not "me too" but "me neither". Are you saying they use it not negatively but positively? Like this:
1) "I think we need more snow this year." "So don't I." ["me, too"]
2) "I don't think we need more snow this year." "So don't I." ["me, neither"]
Which way do they use it?