Do auras really have color and movement to them?
As we know, Gyo can be used to see aura. Assuming it has color, then yes, Nen users should be able to see an aura and its color. 

It is quite hard to tell if there really is a distinct color to aura depending on the user since manga is just black and white. Looking at Volume 33's cover, however, you'll see the following: 

Notice how there's a faint red aura surrounding Kurapika. The animals are from his ability called Emperor Time and you'll see that it is also surrounded by a whitish aura. With this, I think it's safe to say that aura do have color and that they should be able to see it as it is since it was never specified that Gyo users cannot see the aura's color.