Answer
Mittens have less surface area than gloves - for example, there is no fabric between the fingers as there is in gloves. When your hands are in mittens, less surface area is exposed, and they will stay warmer. The situation is similar to that of an apartment building being more energy efficient than single-family housing, because of the shared walls, and having less surface exposed to the weather.
Body parts that are most susceptible to frostbite include extremities that poke out, such as fingers, toes, noses and ears. These have a large surface area exposed to the outside air, relative to, say, an equal-mass amount of flesh in your torso.
