Should AC coolant pipes be mounted on the exterior?
This is the way it's done many times. In new construction they may be put underground but if they fail, they are replaced up the exterior wall and through the attic. I must say that it's a pretty sloppy job though. The installers could have made a better effort to keep them straight and up against the wall the entire way. There are shields that are usually placed over the pipes to hide them and further protect the insulation from the elements (see below). The safety and reliability won't be affected by this installation.
Picture from Metal Roofing Screws.