Ice is water frozen into a solid state. Depending on the presence of impurities such as particles of soil or bubbles of air, it can appear transparent or a more or less opaque bluish-white color.
Ice cubes or crushed ice can be used to cool drinks. As the ice melts, it absorbs heat and keeps the drink near 0 °C (32 °F) (source)
So can hamsters eat ice at all?
No they can’t unfortunately. It is just too cold for them to eat although they will enjoy the fact that it is water based.
If it is cold enough for their water to turn to ice, then it should be thawed so they can drink it properly back in its liquid form.