It isn't just the air temperature that affects the melting rate of snow. In fact, the melting of a winter snowpack is a rather complicated process. In yesterday's Weather Talk, the temperature of the snow, itself, was shown to have a huge impact on how fast it melts. Another key element is humidity.
High humidity melts snow and ice much faster because the humid air squeezes more air molecules out onto the snow surface, where it cools and condenses. This phase change releases heat, which further melts the snow. In dry air, there is very little condensation, so the snow melts much more slowly.
A sunny day has very little impact on freshly fallen, white snow. However, as the snow becomes gray and dirty in spring, it is able to absorb solar radiation, which can enhance melting even at air temperatures colder than 32 degrees.