At a visual inspection the motor mount (side) looks great. That said looks are deceiving.
Once in drive w/brake-on I get the vibration, but could the issue exist and not noticed until drive-train engages? If so, what could that tell us?
If the motor mount is the issue, and it maybe, why does the vibration settle or go away once engine is warm? Things just settle at high temps?
Serious question not being facetious.
If not the mount. what else could make a vibration like that?
If the belt tensioner is working hard cold it be a bad power steering pump? Perhaps, an a/c pump pulley dragging before it freezes or goes out?
The what-ifs are endless I suppose.