This question gives us a chance to revisit the basic issue of how dissolved molecules affect the freezing of water.
Liquid water is a rather disorganized jumble of molecules. There are many ways in which sugar molecules can fit into this jumble. Frozen water (ice) is a regular array of molecules. Sugar molecules don't fit well in that array. So when you freeze sugar water or juice, the sugar stays behind in the liquid water as the ice forms.
Why does that make it harder for the ice to form, lowering the freezing point? Here's a clue- it turns out that the type of molecule dissolved in the water doesn't make nearly as much difference for the freezing as the number of molecules per volume. When the ice forms, the leftover sugar (or whatever) molecules have a smaller volume of liquid to run around in. There just aren't as many different states left for them to explore as there were to begin with.
It turns out that nature has a very deep general principle. Things drift toward forms with the most possible physical states. (This is called the Second Law of Thermodynamics.) It's this principle that ends up determining which chemical forms are most stable.
So having some dissolved molecules in the water tends to favor the form that lets those molecules have the most states- the form with no ice crystals. The balance of factors favoring ice or liquid water is thrown a bit toward the liquid side, lowering the freezing point.
(published on 09/05/10)