A lot of people think it's wrong to wear animal fur, and a sheep skin coat is in the same category because it is made of an animal's skin. People can wear fabrics that come from plants, like cotton or flax. Wool is also acceptable, because no animals die when it is gathered.
No, there isn't anything wrong with wearing an old sheepskin coat. Sheep are not an endangered species. If that was the case, then the ethics of wearing coats made of their skin would be much more questionable. Additionally, people already wear articles of clothing made from wool, yet no one seems to call into question the ethics of shearing sheep for their woool.