In most 3D export formats, colors are written in a straightforward way. You can turn colors on or off using the Write colors checkbox in the Other options panel of the 3D export options window. 

Special considerations for writing colors:

       There are special, more complicated options for writing out colors to DXFExporting_to_DXF

       When you write colors to OBJExporting_to_OBJ, a separate materials file (*.mtl) will be created alongside your OBJ file. Be sure to copy the MTL file along with your OBJ file to the same directory, or the colors will be lost when you import the OBJ file. (Sadly, theres no way to combine these in OBJ.)

       For formats that use materials (LWO, OBJ, and 3DS), a maximum of 1000 separate colors can be written out per file. Its not likely that youll exceed that limit in a single file.

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