This cow seems to be after a tourist.
Now look closer at the picture. Do you see the operatic cow perched on the old well in the background at the very top? It's William Wallace in"cow"nated. Yep, Braveheart, blue face paint and all. Definitely click to enlarge that one:)
Here are a couple of cows in front of City Chambers (these photos all on HIgh Street, aka the Royal Mile).
This first one is on stilts.
This one is called Thistle Cow, near Thistle Street (where there is a shop named Thistle Do Nicely). Coincidentally, it's painted with thistles.
I swear I did not see that phallic looking bollard when I took the photo.