Bar Mitts, out of Carson City, NV, had something new for cold weather riders.  These neoprene hood covers block the wind while keeping the brake levers/shifters accessible.  Simple concept, hit the “more” tab to see a photo from the rider’s perspective…
They have specific models depending on the brand of shift/brake lever you have.
It seems like there’s enough room to do what you’d need to do, but we’re trying to get our hands on (in?) some for a test/review.  In the meantime, just so you know, “riding no hands is dangerous.“