Motor Mount replacement

I have a 2003 GMC Envoy with 76000 miles on it. I heard a louder exhaust noise than normal when I start the truck in cold weather. I had it checked and was told that the exhaust system was OK but that the noise was because the motor mounts needed replacing. I have never heard of this before. Before I spend this money I wanted to see what your reply was to this question. Is it common for motor mounts to have to be replaced on this type vehicle with this mileage and age?

Is the noise there at all times or only when it’s cold? Do you feel a heavy shift and vibration when the transmission shifts? Lastly, can you grab the engine and physically move it back and forth?

Its very unusual that motor mounts wear out that soon but I suppose it is possible.

Does your truck have a secondary air injection pump?
If it does, I’d make sure that it’s not the cause of the noise.