Straight up, your garage door guy is full of shit. I don't care how a metal door is insulated, unless it is EXTREMELY well built, with continual thermal breaks at all edges, it will have dozens of lineal feet of thermal bridging around the edges of panels. Meaning that it may have a "Theoretical (advertised) R value" of whatever the value of the internal foam is, but the fact that the metal outer and inner skins are connected, it's actually a pretty poorly insulated assembly overall. IOW, there is a good chance that it will be more conductive, with less R value than your current wooden door. I just Googled "thermal image of insulated garage door" which resulted in a few clear pics. of the panel edge loss phenomenon in metal "Insulated" doors.
AS others have said, hit ithe cable with anything from fluid film (great shit, BTW) to silicone spray grease, or even WD-40 on a regular basis, nail a rubber sealing gasket to the bottom of the bottom panel, (which will slightly elevate the door bottom out of the slush), and you will get another decade out of the cables this time.
Oh, and if it takes a moment of Googling to find $30 stainless steel cables that would of prevented this problem from reoccurring the FIRST time the guy replaced them, well it appears that he is a dick that is setting you up for a regular screwing.