Well, I don't know Mr. Axl Rose, but I'm sure that he is interested in many things. Maybe even mythology.
Here's a short description of Pegasus...some of which is very interesting. Copied from The Columbia Encyclopedia, Sixth Edition. 2001.
Pegasus, in Greek mythology
in Greek mythology, winged horse that carries the thunderbolt of Zeus. He sprang full-grown from the neck of the dying Gorgon Medusa. With a slash of his hoof, he created the Hippocrene, a sacred spring of the Muses on Mt. Helicon. Hence, he has often been associated with the arts, especially poetry. Pegasus was captured by Bellerophon, who rode him through many adventures. His name indicates a pre-Greek origin.
Notice that Pegasus has often been associated with the arts? Especially poetry? Well, isn't songwriting a lot like poetry? Especially the lyrical aspect?
Or, Mr. Rose might have just thought that it looked cool.