This sort of thing http://www.ebay.com/bhp/handlebar-mitts
actually work very effectively, and have made my hands a whole lot more comfortable on my daily commutes through the winter months.
The same sort of things are essential for hang gliding when it gets cold. Way better than just gloves or mittens.
Also for strollers in Norway.
Any concern that your hands might be trapped to some extent if something unexpected happened? Any downside at all?
Well, they don't look particularly stylish! They are a minor nuisance if you have to make hand signals for turns, since it takes a second two to get the hands back in afterwards.
There is no difficulty getting the hands out in a hurry. And at least on my bike, if I need to use the brake with a hand that is out of the mittens and might not get back in fast enough, grabbing the brake lever through the mitten still works. They are nice because they are basically wind and watertight, and they also insulate the whole length of the handlebar, so that after a few minutes of riding it no longer feels like your hands are freezing from the inside as well as the outside. because of that chunk of aluminum you are holding onto. Another nice feature is that you can wear quite thin gloves inside the mitts, so that you can feel the brake levers and shift levers.