Okay. When I was working at my fomer job, as a habit I would bring gatorade lime rain 20 oz bottles with me and stick them in the freezer to get cold. I figured by my first break, they would be cold enough to drink one, and pop the other one in the fridge to save for lunch. Well a funny thing wouold happen.
I know that frozen liquid expands, so before I would put my warm drinks in, I would open them and take a drink, to give them room to expand if I didn't get to them in time. Now, on my first break, I'd pull the first one out of the freezer, they would be standing upright, and out of force of habit, I'd shake it. All of the sudden, the inside would turn into a slush that was thicker, more dense I think than a slushie type slush. Well it didn't harm the drink in any other way, in fact it made it fun to have a gatorade "slushie." Now what is behind that happening? Is it two different temperatures inside the bottle mixing? By the way, no other flavor of gatorade, Rain or otherwise, would do this.

Fast forward to the other morning. I like to keep a 1 liter bottle of water in my freezer with half of it full. When it freezes, I add water, and have cold water for a long time, something that I enjoy. Well, I had put it in the freezer later than usual, and when I got up in the middle of the night, for a constitutional, I popped an ice cube in my mouth (I have really bad dry mouth,) and saw that the water was at least cold. So I decided to drink a little from the bottle with the ice cube in my mouth. When I started, the water that touched the ice cube started to instantly freeze! I had little ice crystals coming off it. Now is that the same thing?
It was cool I know that. I have never been able to replicate the gatorade experiment with any other beverage, or freezer. There must have been something with the temperature level of the freezer at work, combined with the water content of the drink.
Anybody have any theories?

I have a hunch that maybe sugar has something to do with it. I know sugar helps to keep ice from forming at the freezing point, so sugar liquids requires a cooler temp to freeze completely... thus the slushy texture happens with soda too. The saliva in your month may have also created a similar reaction just in your month, but I think that reactions was different than your Gatorade trial.

Cool. I know that salt does the same thing, in fact I learned an old bar trick to getting cans of (Well beer, but I use it for sodas,) cooled quickly. Take a container, fill with ice and water, and pour a handful of salt in. Add as many cans as container can hold and stir for two minutes. The cold energy transfers into the cans, and they go from 80* to 40* in that time, plenty cold to serve. But sugar? Hmm.
The range of sugar/liquid must be very small though, because I was unable to replicate the experiment with juice, other gatorades, or even soda. But I don't want to try the soda thing again. That thing about shaking and carbonation is not a good idea...

Right, soda in the freezer is not a good thing as it can explode. So it's best to know that Sugar and Salt work differently. Salt (NaCl) is ionic and is much better at lowering the freezing point and defrosting ice because the charged particles are much more effective in preventing ice crystals from forming. Sugar is neutral thus is better for making slush at freezing point temperatures.

Well, best wishes in your experiments.