Urinating in SpaceAs it turns out, the answer to this question is known. When astronauts urinate in space and release the contents, the urine rapidly boils into vapor, which immediately desublimates or crystallizes directly from the gas to solid phase into tiny urine crystals. Urine isn't completely water, but you'd expect the same process to occur with a glass of water as with astronaut waste.
How It WorksSpace isn't actually cold because temperature is a measure of the movement of molecules. If you don't have matter, as in a vacuum, you don't have temperature. The heat imparted to the glass of water would depend on whether it was in sunlight, in contact with another surface or out on its own in the dark. In deep space, the temperature of an object would be around -460°F or 3K, which is extremely cold. On the other hand, polished aluminum in full sunlight has been known to reach 850°F. That's quite a temperature difference!
However, it doesn't matter much when the pressure is nearly a vacuum. Think about water on Earth. Water boils more readily on a mountaintop than at sea level. In fact, you could drink a cup of boiling water on some mountains and not get burned! In the lab, you can make water boil at room temperature simply by applying a partial vacuum to it. That's what you would expect to happen in space.