In the future, it is plausible that we can change the physical appearance of a living animal by editing DNA?
This article explains that scientists managed to change the DNA of adult laboratory mice with an inherited liver disease, thereby curing them of the disease.


Yes, Read about CRISPR-CAS9 method of gene editing. This is not the only method which can achieve this. There are many others like TALEN or Zinc Finger. 


  If we used this same method to edit our hair follicles, could we alter our hair color?


Yes, similar studies like this has already shown this potential but using different method as mentioned in article you linked. 


  The new hairs would have altered DNA, and come out a different color depending on what the cells have been altered to. 


For this you need to express such constructs in cell specific manner. Drosophila geneticists are doing such things for long long time. 


  And then, is it possible to change the physical size and shape of a living animal by editing DNA? For example, if an animal has porous and small bones, is it plausible that we could edit its DNA so that its bones start to become more dense and thick? The physical appearance of the living animal would be changed, since the bones are larger than before. 


Plausible but remember such characteristics are controlled by many factors which will be hard to control. Plus there will be age/environmental/epigenetic factors which you can't control with such techniques.


  Along these lines, could we then edit DNA of an adult human to change bone structure so that we have sharper noses? Larger eyes?


Most of these techniques required change in germ cells. Hence it will be difficult to implement such techniques in adults. However 'ideally' you can use techniques like RNAi which can be triggered by specific inducers at any stage of life (like temperature sensitive UAS-Gal4 system used in fly genetics).