I have poor circulation, so in the winter my hands get cold. I see people riding with no gloves when the temperature is in the 40's and I wonder how their hands feel. I want to stop them and say, "There are these great things called gloves, you put them on your hands when it is cold and the keep your hands warm!" I sometimes feel that I should carry around gloves to give away, but who knows if the gloves would even be used.
A couple of years ago I got tired of cold hands and I went out and bought mountaineering gloves. They are ridiculously warm - lobster claw inner glove and thick mittens for the outer layer. Even in sub-zero weather, they keep my hands warm as long as I start off warm. These mittens are bulky and I found that it was very difficult to change gears on my winter bike, which had brake mounted shifters, so this fall I had the shifters switched to the bar ends. I think that should solve the problem. Bar end protectors are a great option, although I have only used an older model which were wind resistant but not insulating. Now you can get a wide variety for any kind of handlebar. Rechargeable heated gloves are available, but I have not tried them. I am not a big fan of chemical hand warmers. They don't always work, especially if they are a couple of years old. Also, they are uncomfortable inside a glove and don't keep your thumb warm! Most of my cold riding is in town, and if frostbite threatens, I know to get inside right away. Most McDonalds and some convenience stores have warm air blowers for drying hands. You can use them to warm your hands and also to warm your gloves or mittens. At City Market, in Burlington there is a hot air blower in the alcove between the inner and outer doors. When I am done shopping I park myself in front of the blower and warm my hands before I go outside. In cold weather, locking and unlocking my bike becomes a challenge. I wear inner gloves so that I can do the unlocking without my hands getting really cold. At home, I go out to my shed, unlock my bike and then return to the house to warm up my hands before leaving. I usually carry an extra pair of gloves or mitten with me. Gloves can get wet with slush even when it is cold, and that often reduces their effectiveness. Also, it can suddenly get warmer or. colder and I want to be able to adjust my gear accordingly. I usually pre-warm my gloves and or mittens with a blow drier. I have to start off with warm hands, or they just get colder even if my core warms up. It is quite possible for me to be sweating from riding up a hill while my hands remain ice cold.