That's a very interesting question that is unexpectedly nuanced at first glance. We are often taught that water takes on three forms- as liquid, solid, and vapor- and that you find these forms at particular temperatures (i.e. ice below 0 degreed C and vapor above 100 degrees C). But it turns out that the state of water depends on both temperature and pressure. The common temperatures we know ice and vapor to form are only true for atmospheric pressure, which is the pressure most everyday things happen.

How do we know which phase water is?
People have figured out using thermodynamics the dependence of phase (what you call the state of water) on temperature and pressure, and put them on graphs called phase diagrams. A phase diagram for water can be found here. By picking a particular temperature and pressure, you can figure out what phase water is.

There are several key features in a phase diagram. The lines, phase boundaries, that separate the regions of ice, water, and vapor are lines of two phase coexistence. That means at temperatures and pressures along the boundary between water and ice, both water and ice can be found at the same time in equilibrium with each other. Most of the time these phase boundaries have positive slope. But water is quite special; the phase boundary between water and ice is slightly negative. This captures the fact that water expands in volume slightly upon freezing. The triple point is where all the phase boundaries intersect and marks a special temperature and pressure where all three phases exist in equilibrium. There is also another interesting point called the critical point. Pressures and temperatures above this point result in an alternate phase called a supercritical liquid where liquid and gas are indistinguishable.

If you're further interested, there are also phase diagrams for a whole multitude of materials, such as multicomponent systems (e.g. mixtures of elements or compounds, such as alloys). They pretty interesting to look at (a good example here of mixing silver and platinum), and predict how things mix at different temperature. It's a whole area of research and study!

Why is the phase dependent on temperature and pressure?
A phase can be thought of as how much the species can wiggle around and how well bonded adjacent species are to each other. For example, solids have closely packed species that rigidly vibrate and gases have minimally interacting species that whizz about. Temperature is equivalent to thermal energy, so the higher the temperature, the more energy the atom/molecules have to wiggle around. Pressure does the opposite. The more pressure you apply, the more you push together the atoms and force them to be move rigidly. There are other factors that I've left out, but that is the general idea.

So in answer to the original question, you can choose whatever phase you want water to be if you choose the right temperature and pressure!

Well, it turns out temperature isn't the only thing that's important for determining the phase of a compound; pressure is important as well. This is what phase diagrams describe; for example, the phase diagram of water is shown here: h2o phase diagram

The point is that if you keep the pressure fixed (at, say, atmospheric pressure), then once you cool down water enough to freeze it, it will stay frozen no matter how low you make the temperature. However, water has the interesting property that its frozen form is less dense than its solid form; that means that if you take frozen water and compress it while keeping its temperature constant, you can force it to melt (you need a TON of pressure to do this, though). You can even lower the temperature as you do this, as long as you increase the pressure fast enough.

So the short answer is that as you decrease the temperature of a block of ice, it will remain ice, unless you also subject it to very, very high pressures.

Great question! Assuming that the pressure of the system were to remain constant throughout this cooling process, water would remain as ice no matter how cold we lowered the temperature. Interestingly, if we were a bit below freezing temperature at 0 °C and we started to lower the pressure, at some low enough pressure the ice would sublime straight into a gas (without passing through a liquid phase). Scientists study this interesting phase behavior of water and other substances, and map out a temperature versus pressure diagram, called the phase diagram.

If you continue to decrease the temperature, water will always continue to be solid ice. However, ice turns out to be much more complicated than you might expect, and depending on the pressure, you can have many different forms of ice. Depending on the pressure, different structures of ice become stable, so there can be phase changes. However, there have been no experiments that have shown solid ice transforming to a liquid when it is cooled further.

At temperatures below the freezing point water will stay in solid phase as ice. You can see from the phase diagram for water in Answer #2 (from page: equilibria phase rule). This shows the phase of water versus both temperature and pressure, at pressures of 1 atmosphere (standard air pressure around us) water will be solid below 0 degrees Celsius.

I'm not sure exactly what you mean by the ice state limit, so I'll do my best to explain this with the graph in Answer #2. click here

On the y-axis is pressure. 1atm is standard pressure, so along the 1 atm line, you can see that as temperature (x-axis) increases, ice becomes liquid water (at 0C), and liquid water becomes water vapor (at 100C). If you keep ice cooling even further it remains solid ice all the way down (staying along the 1atm pressure line--changing increasing or decreasing the pressure a lot may change this as shown on the graph).

The bottom line is that ice stays ice as you continue to decrease temperatures into the negative C, and will not turn back into water at constant pressures. Interestingly, the crystal structure of ice can change though, based on the pressure. That means essentially that the molecules pack in different shapes. Typical ice that we see is always ice-1, but under extreme pressures, the packing of the molecules can change to make ice-2, ice-3 etc. If you've ever read Kurt Vonnegut's book Cat's Cradle, it talks about an ice-9. There IS an ice-9, but it only exists at remarkably high pressures and doesn't act the way it does in the book. But, it's an interesting bit of science fiction (and a great novel too).

At atmospheric pressure, (pure) water below 0 Celsius will be either remain a solid or sublime and become a gas, not a liquid. Liquid water can exist at lower temperature, but only at higher pressure than at the surface of the Earth (or if it contains salt or other solutes).

t is possible to supercool liquid water so that it still exists as a liquid even though it is at a temperature where the solid state of water (ice) is stable. This supercooled liquid state is what is known as a metastable state. At temperatures below freezing point, the solid state is thermodynamically stable (lower in free energy) than the supercooled state. However, the system can be kinetically trapped in this metastable state.

To supercool water, you can take distilled or purified water in an unopened water bottle (impurities can serve as nucleation sites for solid ice formation, so we want to avoid these). Cool the water in a freezer for several hours, and then carefully remove the bottle from the freeze. If the water inside is already solid, then you will have to re-do this cooling process. To get it to crystallize (form solid ice) from the supercooled state, you can shake the bottle or pour it over ice.

The temperature vs. pressure phase diagram of water shows us that at about 1 atmosphere of pressure (which is nearly equal to the ambient pressure at sea level) liquid water turns into ice. As we continue to lower the temperature though, there isn't much apparent change according to a simple phase diagram. Our ice will stay ice as we cool.

Now, there are ways to keep water a liquid below 0oC at room temperature while still maintaining the same pressure. You could add an impurity like salt. Salt is often used on roadways to keep ice from freezing and making the ice slippery.

You could also have "supercooled" water. To turn into ice, the liquid water needs a nucleation point. The nucleation point is just something that ice crystals can start growing on. If there's no "seed" for the ice crystals to grow, they will just stay as a liquid. As soon as a particle of dust is added or the container is shaken, the water, which can be much lower than 0oC, will nearly instantly freeze. You can supercool water yourself, but it's a very delicate process. The easiest way would be to take an unopened bottle of purified or distilled water and stick it in the freezer. In a few hours, the temperature will be below freezing, but the water will still be a liquid!

You could also increase the pressure. You might notice something interesting to the phase diagram of water compared to other materials. As the pressure is increased, the melting point decreases. This may seem strange, but without this, life would be much, much different (or even non-existent!). That means you could increase the pressure and have ice turn into water even as you lower the temperature below 0oC. Food scientists have applied this principle to thawing: thawing with high pressures can thaw food nearly three times faster than at normal atmospheric pressure.

One interesting tidbit that the water phase diagram does not point out is all of the different crystal rearrangements of water. Hydrogen and oxygen have a little bit of freedom to distort their bonds and change the crystal shape. There is a lot of research on finding new rearrangements of water and exploring their properties. Researchers call these rearrangements "polymorphs" (which literally just means "many shapes"). If you're familiar with Kurt Vonnegut's Cat's Cradle, he writes about a fictional form of ice that freezes at room temperature. If you seeded water on Earth with this ice, all water would immediately freeze solid at room temperature and could destroy all life! Fortunately, there aren't any forms of ice like Vonnegut's creation, but there have been as many as nineteen different polymorphs of ice discovered thus far!