The truth is that the muzzle of a cat does sometimes turn gray in old age (I have seen it first hand) and a study concluded that dog muzzles turn gray due to stress and anxiety (and I presume in old age although there is an overlap here).
The point is that the question in the title is incorrect. The study that I have referred to concerns dogs. That’s because dogs are far more often chosen for studies of this sort because they are easier to handle.
However, cat owners will notice that their elderly cat might have turned gray around the muzzle although it seems to me that the graying is less extensive than in dogs.
The question that I have is how much of the graying is due to stress and how much due to old age. You could argue that old age and increased stress might go together.
The fact that stress causes hairs to go gray in dogs and possibly in cats tells us that ‘pets’ are not that dissimilar to us in many respects. There is not much more to say really.
Click on this link to read about stress and dogs (or pets generally).