Can I install a service panel on an exterior wall?
I have never had an issue of a panel on an exterior wall infact over 95% of panels I have installed are on exterior walls or basement walls. If the inspector is concerned about condensation ask if he would allow a small device for dehumidification or low wattage fire rod would be allowed, many years ago I started putting low wattage fire rods in outside panels close to pools or water sources this keeps the panel just warm enough to not condense the moisture and extends the panel life. 

But as I know of no direct code reference I would ask the inspector to cite the code reference that requires insulation. 

I do know inspectors that try to pull crap on home owners and when I moved to a new county I had not worked in I think the inspector had 4 write ups and one would be considered a red flag (power down) I asked him what the code reference was because I had not touched that part of the structure, he stammered and said it was always that way I grabbed an older code book that I had at home and flipped it to the section and said no you are wrong and we can call the chief electrical inspector is you want to keep any of your opinions on the record. He then asked what are you an electrician and I gave him my number he wrote up a new inspection report with all items passing. So I know they do it maybe not all but in my location they do.