If it is silver nanowire it is likely reflective, hence the light of the optical microscope might reflect light off the wire. Small variations in the nanowire or its position might give rise to the perception of different colours in the reflection.
I’ve seen similar effects and would like to see a physics answer.. I suspect the color isn’t due to a change in the optical constants but due to wire diameter. Does the substrate material affect the color?
As nanowires are narrow, completely intransparent objects, physical effects like diffraction, dispersion and chromatic abberation of the microscope lenses, as well as reflection of ambient light should be taken into account.