Density of an object is increased with the cooling, but this is not completely applicable in the case of fresh water. It is densest at four degree Celsius and if water is further cooled its density keeps on decreasing. So a substance having less density or less mass per unit volume than other substances in the mixture always floats. That is why ice floats on the water. Ice is 9% less dense than the water; it covers about 9% more area than the fresh water. A quantity of ice always weighs less if we compare it with the same quantity of that substance in its liquid state.
When an object is submerged in water it displaces the mass of water that is more than its own mass. So a force pushes the object upwards till the mass of object becomes the same to the mass of water displaced. So ice always floats on the surface of water. When lakes and river are frozen ice is pushed upward and fishes survive in the water under the ice.
When water changes to ice crystals a network of water molecules which were close moves apart from each other causing the density of ice to decrease by 10%. Normally with the increase in temperature density decreases and with the decrease in temperature density increases. But it does not happen in the case of ice.
In water each molecule is bonded with 3.4 of other water molecules approximately with hydrogen bond while in ice each molecule is bounded with four other molecules in hydrogen bond. If we add sugar or salt to the water the density of the ice can increase to such an extent that a cube can sink in the water.
Because the ice floats on water we can say that the ice is less denser than water and covers more space than the water. That is why we see that a glass jar filled with water burst when the water in the jar changes to ice.