The belt is not necessarily shredding, although of course it could be.
More likely, there is some belt slack between the crankshaft and the exhaust cam. Because of that, during the short time when the exhaust valves are closing the spring can push the camshaft around faster than the timing belt is turning. The cam pulley actually pushes the belt towards the intake side faster than the intake cam pulley is turning. That means slack in the belt can build up between the pulleys and the belt gets pushed up against the cover.
I don't know why this would start suddenly, or why it is worse in cold weather. My theory is not completely developed.
However the best thing to do, is when you replace the belt, whoever does the work should follow the procedure in the Gates Timing Belt Replacement Kit. This means they need to loosen the cam pulleys from the camshafts, (without letting the camshafts rotate!) and rotate the pulleys to take out all possible slack starting at the crank and working around CCW. I think that was the order.... Anyway read the directions. Then tighten the cam pulleys back onto the shafts.
My car did this noise for many years until I had the belt replaced properly and now it is much quieter.