Using your phone during winter without a pair of gloves is not fun. There are plenty of touchscreen gloves available on the market which let you use your phone while keeping your hands warm. These 2 iPhone handwarmers can also keep you warm on extremely cold days:
Hand Warmer + Power Bank Battery: applies instant heat to your hands but also has a 6000mAh battery to charge your phone. It has a built-in flashlight too.
Handwarmer with Smartphone Recharge: this hand warmer not only takes care of your hands but also charges your phone. It is compatible with iPhone, Android, and Blackberry devices.
There are plenty of other rechargeable hand warmers around. The above products are compact and can serve as a backup battery for your iPhone. They are nice to have on a cold winter day.