I'm just getting into light painting, and as was said, this photograph doesn't qualify as something "paintable". For me light painting has more to do with artificially lighting sections of a photo during the exposure.
With this photo what you likely want is something more akin to a composite and not necessarily the HDR approach suggested. It would require multiple exposures, one exposed for the stars as yours is, and one (or possibly more) that exposes for the the mountains, ignoring the fact that it would make for star trails everywhere else. Using Photoshop you would stack the additional photo(s) as layers on top of this photo and use masks to paint in background areas that were exposed differently. Takes a bit of practice to learn how to blend the edges in a way that looks natural, and how to vary mask opacity layer to layer, but it's very doable and becomes easier with practice.
This differs from the HDR approach, which would be troublesome given the ghosting you'd get from the star trails in the images exposed for the mountains. Some software would handle this more effectively than others, but I suspect it would be more problematic than the composite approach.