Why does ice float but cold water sink when in room temprature water?

It's a question of density, or compaction of the molecule.  The density of most materials decreases with increasing temperature, because heat increases molecular agitation and makes the molecules move a bit further from each-other.  The solid state is usually the densest, where the molecules are arranged in their optimal, most tightly-packed, immobile configuration; and in a gas, molecules are furthest from each-other and zoom around freely.

So, cold water is a bit denser (heavier) than room temperature water and falls at the bottom. But ice is a solid exception, and is not denser than liquid water: it is actually less compact than water, and therefore weights less for the same volume. Thus, it floats... (Icebergs, anyone?)