If you put a bottle of vodka in your freezer, the liquid thickens, but it won't turn solid. This is because of the chemical composition of vodka and a phenomenon known as freezing point depression.
The Chemical Composition of Vodka
Mendeleev, the chemist who devised the periodic table, standardized the amount of ethyl alcohol-- or ethanol--in vodka when he was the Director of the Russian Bureau of Standards. Russian vodka is 40 percent ethanol and 60 percent water by volume (80 proof). Vodka from other countries may range from 35 percent to 50 percent ethanol by volume. All of these values are alcoholic enough to significantly affect the temperature at which the liquid freezes. If it was pure water, it would freeze at 0 C or 32 F. If vodka was pure or absolute alcohol, it would freeze at -114 C or -173 F. The freezing point of the mixture is an intermediate value.
Ethanol and Freezing Point Depression
When you dissolve any liquid in water, you lower the freezing point of the water. This phenomenon is known as freezing point depression. It is possible to freeze vodka, but not in a typical home freezer. The freezing point of 80 proof vodka is -26.95 C or -16.51 F, while the temperature of most home freezers is around -17 C.
How To Freeze Vodka
One way to get your vodka extra-cold is to place it in a bucket with salt and ice. The contents will then get colder than ordinary ice, as an example of freezing point depression. The salt brings the temperature down as low as -21 C, which is not cold enough to freeze 80 proof vodka but will make a vodka-sicle out of a product that is slightly less alcoholic. Salting ice is also used to make ice cream without a freezer.
If you really want to freeze your vodka, you can use either dry ice or liquid nitrogen. Surrounding vodka with dry ice drops the temperature down to -78 C or -109 F. If you add chips of dry ice to vodka, the sublimation of carbon dioxide will form bubbles in the liquid, essentially giving you carbonated vodka (which also has a different flavor). Note that, while it's okay to add a small amount of dry ice to form bubbles, actually freezing the vodka would produce something too cold to drink (think instant frostbite).
If you pour a bit of liquid nitrogen into vodka, you'll get fog as the nitrogen evaporates. This is a cool trick and may produce bits of vodka ice. Liquid nitrogen is extremely cold, all the way down to -196 C or -320 F. While liquid nitrogen may be used by bartenders to produce (literally) cool effects, it's critical to use caution. Frozen vodka is colder than a freezer, which basically makes it too cold to ingest!