Ug boots (also spelt ugg boots or ugh boots) are more accurately described as being made of sheepskin, not wool.
The wool is just the inside lining of the boot which happens to be attached to the sheepskin. Sheep tend to be more forthcoming with wool than their skin.
The top of an ug boot is often rolled down to present a "collar" effect where the wool lining can be seen around the top of the boot. The wool is often dyed with a colour, such as grey, brown or pink.