What Actually Happens
There are several things that help the hot waterl freeze faster than the cold water. Here are what is thought to be the most significant factors:
Layer of ice forms on the top of the cold water.
The hot water is more likely to be supercooled. This means that the hot water's temperature is more likely to cool to temperatures below zero degrees Celsius. In the cold non-supercooled water, ice crystals form and float to the top, forming a sheet of ice over the top of the water, creating an insulating layer between the cooler air and the water. This ice sheet also stops evaporation. In the hot water that has become supercooled (thus, no longer hot) the water, when it does freeze, freezes throughout, creating more or less of a slush before freezing solid.
Why is hot water more likely to be supercooled? Because hot water is less likely to contain tiny gas bubbles. Gas bubbles form from dissolved gasses as the water cools. When the hot water was heated, these dissolved gasses may have been driven out. In cold water, ice crystals use the tiny bubbles as starting points for formation (in physics, we call them nucleation points). But in the hot water, there are no bubbles, so there aren't as many starting points for the ice crystals.
Dissolved gasses also lower the freezing point. Since heated gas is less likely to contain dissolved gasses, it's more likely to freeze first.
Simple really.

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