On top of the cold water, a layer of ice forms. It’s more likely that the hot water will be supercooled. This means that the temperature of the hot water is more likely to drop below 0 degrees Celsius. Ice crystals develop and float to the top of the cold non-supercooled water, forming a sheet of ice over the surface and creating an insulating layer between the cooler air and the water. This ice sheet also prevents water from evaporating. When supercooled (therefore no longer hot) water freezes, it freezes evenly throughout, generating a slush before freezing solid.
Why is it more likely that hot water will be supercooled? Because small gas bubbles are less likely to form in hot water. As the water cools, dissolved gases produce gas bubbles. These dissolved gases may have been forced out when the hot water was heated. Ice crystals grow in cold water using small bubbles as starting sites (in physics, we call them nucleation points). There are fewer beginning places for ice crystals in hot water because there are no bubbles.
The freezing point is also lowered by dissolved gases. Because hot gas has less dissolved gases, it is more likely to freeze first.
The hot water in the bucket evaporates more faster than the cold water. This accomplishes two goals.
To begin with, evaporation is an endothermic process, which means it requires energy to evaporate. When a water molecule evaporates, it leaves the water’s surface and flies into the atmosphere. In other words, the molecule transformed heat energy into kinetic energy (energy of motion). Because hot water evaporates more quickly than cold water, it loses heat energy more quickly than cold energy.
Second, because some of the hot water evaporates, there is less water that must freeze.
The surrounding snow will be melted by the hot water pail. Later, when the weather cools, the snow around the pail will harden and “touch” the pail more closely. The cold water pail is therefore merely sitting in fluffy light snow, while the hot water pail is encased in an ice-crust that fits it perfectly. Obviously, the ice-crust will conduct the cold better than the fluffy snow.