I recommend cycling gloves for a couple of reasons. Most cycling gloves are cushioned on the palms, providing proper circulation in the various hand positions on your handlebars. In the winter months, full fingered gloves are a good idea or cycling mittens for more extreme conditions. For those super cold days you decide to brave, try wearing a pair of wicking liner gloves underneath your mittens/gloves.
Hand warmers are for camping, not cycling. They will get far to hot underneath your gloves, plus your dexterity and mobility of your hands will become greatly impaired while you try and push the warmer out of your palm. My opinion – let them remain behind the counter at the gas station, you don’t need them.
Since the feet are pedaling circles and churning through the cold air more than the rest of your body, they need to be protected from the cold. Like the head, body heat is lost to a large degree through the feet. For cold-weather riding, use a heavier thermal cycling sock that wicks moisture and retains heat; choose socks made from synthetic fabrics.
Cycling booties slipped over your shoes are great in cold weather. The booties are designed to accommodate your pedal cleats, and insulate your foot and ankle as well. For days that aren’t cold enough for booties, wear toe covers. Toe covers accomplish the same thing that a windbreaker does for your chest: they keep the cold air from penetrating your foot.
Be warned, If you are wearing neoprene booties you may want to grab your summer riding socks in lieu of the winter woolies that keep you ohh so toasty. The wool will get heavy with sweat from lack of breath-ability and will ultimately make your feet freeze upon your first rest stop, once the cold hits. Wear wool on days when you go for the toe covers, and for post ride comfort.