Yes, that is the real reason to wear a hoodie, however, there are others. They make great concealment from video cameras and witnesses when one is committing a crime.
Clothing can be a signal and it can be useful to criminals. A relative of mine managed a retail store, and she knew when someone entered the store all covered up with a large coat and wearing baggy pants (in the scorching heat of summer), that they were shoplifters.
As the old saying goes, “Clothes make the man.”
That is why banks have a sign stating that you have to remove all hats, hoods and sunglasses before you enter, they don't care how cold it is outside.