Water is strange. Unlike most compounds, its solid form is (normally) less dense, and of a larger volume than its liquid form. Because of this, its very difficult to compress water, because normally there isn't really anything to compress it into. But the story of ice is a bit different from the snow and hail we see falling outside of our windows during these winter months. In fact, ice has many different forms, depending on the conditions it forms in.
The ice we commonly know is called Ih - a common ice type with a hexagonal structure. But as you can see from the picture, there are many different types of ice. Ic is also a (relatively speaking) common ice type, with a cubic structure that can be present in the upper atmosphere. In total there are 15 different types of ice, all forming at different pressures and temperatures, all with different crystal structures, densities, and electrical properties. For example, while water is hard to compress, when put under great enough pressure at normal temperatures, can form into ice IV (not pictured), a denser form of ice. While most variations are just density and structure based, certain forms (like ice XI) have ferroelectric properties, which is something I looked up and failed to understand, but it sounded interesting. And noticing the lower pressures, below ~1 kPa (about 1/100 of normal sea pressure), liquid water fails to exist, and water vapour will undergo deposition straight into ice below this point.
As we head into winter, it's interesting to note the complexities of such a common substance. It can take on many forms with many properties, and I think that's pretty cool.