What is the copyright of the MathOverflow logo? Is it in the public domain? In this site they say that "most simple logos simply do not have the required level of creativity to be considered copyrightable", so I imagine that to be the case for the MO logo as well.
There is neither an officially claimed copyright or trademark on the MathOverflow icons or logos. That said, we would really like anyone who intends to use it to explain their proposed use (here on meta is fine), and obtain the approval of the community (and potentially the board) first.