Export as DAE

DAE files are commonly called Collada files.
You can export DAE from any version of SketchUp.

Make an object in SketchUp, say a box. You do not have to make a component of it, since that makes no difference now.

Give the object a skin. Use a material like a groundcover on all sides.
This is necessary for two reasons. In the first place it will make differences between the various export options clearer. And second: an object not having a skin or an incomlete skin might show in Photoshop (partially) as a TIN, as we shall see later (TIN: Triangular Irregular Network; search on sketchup + tin.) or as a wireframe.

File > Export > '3D Model' > 'COLLADA File (*.dae)'.
This will result in the export of a DAE file of course, but also a JPG of the skin (see above). There will be no JPG if instead of a groundcover or such (a "3D" material) you use a color ("2D"), though the export of the color works fine. Later you shall see why we want to have a JPG.

(Export a box or such without skin, and compare.)

In Photoshop do File > New, and set the size on 1.000 x 1.000 px or such. No background.
Do 3D > 'New 3D-Layer from File' and choose the DAE file with skin. Click Open. This works fine. Save the file as PSD.

 (Here in Photoshop I have already changed the skin)
(Do the same with the box without skin and compare. Works fine using DAE.)

In Photoshop open both 3D and Properties panels (see above).
In the 3D panel select the layer with the same name as the skin. See that then, in the Properties panel, you can change to another skin. Do so. As you can see above, the new skin ("grass") is applied to the whole object, although we did not make that into a component.
Save the file as a PSD but of course with another name now. 

Do 3D > 'Generate UV's' and after that 3D > 'Export 3D-Layer' and choose DAE.
Have a look at all the files you have produced. See above. The two files at the right are the UV PSD files. In early versions of Photoshop CC there was one file, a JPG.

In SketchUp do File > New, and then File > Import. Select 'Colada Files (*.dae)', choose the DAE exported from Photoshop after changing the skin and click OK.

[SketchUp 8 / Photoshop CS6:]
Disregard a possible warning.
See that the result is far from correct. Even if you export the unchanged PSD as DAE, it will not import correctly in SketchUp, although the export does produce a JPG of the skin.

[SketchUp Make 2015 / Photoshop CC 2015:]
Although the files are not JPG but PSD, it all works fine. See above and below.

Something which has changed in SketchUp Make 2015, compared to SketchUp 8, is that when importing something, you get a so called Loaded cursor, as to be able to position the import.

[SketchUp 8 / Photoshop CS6:]
If you leave one or more sides without a skin in SketchUp, then you will be able to apply a skin to those sides in Photoshop, but as soon as you rotate the object things go wrong.

[SketchUp Make 2015 / Photoshop CC 2015:]
See below now, in Sketchup, the box with only two sides covered, 1 and 2.

See below, exported as DAE and imported in Photoshop.

Hope to get comments on that...
The grey rectangle in front is the shadow. Where the 'botom' and the third side came from (as they were not covered with a material) I don't know.

NB Same problem using more then one material.