Thank you Adam, you pointed me in the right direction. :-)
Setting the right color property to white once again at the end does the trick of refreshing even the exponent color.
Turns out the program I used to generate my graphics (slover from the SPM package for neuroimaging) does not use the colorbar object at all, but instead generated a subplot axis object. Hence my exponent in question is the y-axis exponent of that object and as such does not supply a handle by MATLAB default. While the axes were created with the color set to white ( axes(...,'Ycolor',[1 1 1],...) ), the exponent will only turn white after explicitly setting the y-axis color to white once again after the figure was created and filled with data. Well...
myCbarHandle.YAxis.Color = 'w';