Ice doesn't absorb Oxygen. You're used to ice which is made from snow. Snow DOES trap atmospheric air. As snow sits from year to year and more snowpack builds up, it compresses to firn and most of the trapped air is squeezed out. With time, more snowpack and pressure finally causes much of the trapped gas to be incorporated into the crystal lattice as clathrates - Nitrogen, oxygen, CO2 Argon, etc...

Ice doesn't float because it contains oxygen or any other trapped gas. it floats because the rigid crystal lattice of frozen water (ice) ice is BIGGER than the chaotic and interlocked lattices of liquid water. This is unusual.

Yes, melting ice releases some trapped air bubbles, but the volume of air (~1%) is far from sufficient to cause ice to float so well (~10% density difference).

Even old "blue" ice floats.