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This is an interesting question! Before I give my suggestion: let me first say that I am not a real coder, I haven't a clue about PHP or or mySQL, and this suggestion may be very complicated for someone who hasn't Xooped a lot (and it may not even work...)
Here's what I would do. Have your users upload their logo as their avatar (make sure to eliminate the minimum post requirement to upload avatar and allow a large enough image size). Then you will have to hack the theme you are using to show your standard logo UNLESS (the user is logged in AND the user has uploaded their own avatar). Of course, this could lead to some goofy looking web pages if the user's avatar is too big or too small...
This is the name of the variable that refers to a particular user's avatar: $user_avatarurl. So, to refer to it as an image using HTML you would write something like
. The conditional statement that would determine if the user is logged in AND has uploaded an avatar is beyond me but shouldn't be too tought to figure out if you know what you're doing.