Wire up your hat with infrared LEDs for even more fun.
Tried that. It's only the lowest, shittiest cameras these days that don't have an infrared filter on them. Buddy of mine is Ashton Kutcher's next door neighbor and we actually built some prototypes; that low-pass has been commonplace since the original iPhone.
IR illuminators will absolutely blow out IR cameras but IR cameras are generally getting used less and less for daytime capture for the simple reason that they can be blown out by IR illuminators. They sort of work with old-school security cams and don't work worth a shit against paparazzi. Expect that any video stream used for facial recognition is going to be paparazzi-grade, not 250 TV lines of 15 frames per minute.
This will happen. If it's not already to some degree, it will. The question will be will people care enough to do anything at all about it. And the best part is that they only need one shot of your face with a geo tag for it to be market relevant data. You must have a 100% perfect defense to have any defense at all really.