If you have a dish of ice and a dish of water in a room at exactly 0 the ice will very slowly melt but the water won't freeze. At -1 the water will freeze. Quite amazingly, under the right pressure conditions, there can be a moment (called the triple point) where water can exist as ice without melting, water without freezing and gas without condensing. So you could have a box with steam, liquid water and ice without any of them changing phases. http://en.wikipedia.org/wiki/Triple_point
Going back 50 years old high school physics, I think it's due to the direction that heat travels - cold to hot, hence at zero, heat is travelling from minus to zero and hence ice is melting. A lot of theory has changed since my days were spent learning defunct information so they may have a newer explanation now.
In just one day, 200 million work hours are consumed by women collecting water for their families. Unsafe water kills 200 children every hour.
Well no physicists here so I went to google and found I was wrong. Heat travels from hot to cold, so my explanation doesn't work, but the theory does. Over to the brains trust
crystallization of pure liquids usually begins at a lower temperature than the melting point, due to high activation energy of homogeneous nucleation. Freezing does not start until the temperature is low enough to provide enough energy to form stable nuclei. The melting point of water at 1 atmosphere of pressure is very close to 0 C, and in the presence of nucleating substances the freezing point of water is close to the melting point, but in the absence of nucleators water can super cool to 40 C before freezing.
"Swampy" Marsh never did a hammie and could never touch his toes. There's something to be said about inflexibility after all.
